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Exercice 11. Let D be the unit disk in R2, D = {(x, y) ∈ R2, x² + y² ≤ 1}. Suppose X and Y have joint pdf f(x, y) = c if (x, y) ∈ D and zero otherwise. (a) Find c. (b) Find the marginal pdf fx and fy. (c) Are X and Y independent? (d) Find E(X) and Var(X). (e) Find the covariance and correlation…
3 1 point Which of the following statements is TRUE about sample size? Sample size is only important in observation research, not experimental research. A large sample size decreases the likelihood that the results of your experiment will be influenced by random Sample size is not that…
Exercise 9.1- Decide whether or not each statement is necessarily true. 1. If X and Y are independent discrete random variables, then $f_{XY}(xy) = f_X(x)$. 2. We repeatedly toss a fair coin. Let U be the number of trials needed to get the first head and V be the number of trials needed to get…
20) 10 pt. Maria has been crossing prize Tea Roses and has created a purple rose by crossing an American Beauty Red with an Amsterdam Black. She suspects that the red and black alleles are incompletely dominant. She shows you the following data obtained from a large number of crosses. Perform a…
Example. The probability that a student passes the written test is 0.7, find the probability that the student will pass the test on the fourth try.
(i) The joint density function of X and Y is given by $$f(x, y) = \begin{cases} 2e^{-x}e^{-2y} & 0 < x < \infty, 0 < y < \infty \\ 0 & otherwise \end{cases}$$ compute: (a) P(X > 1, Y < 1) (b) P(X < Y) (c) P(X < a)
A box contains 50 balls numbered from 1 to 50. If 10 balls are drawn with replacement, what is the probability that at least two of them have the same number? Answer:
Which of the following is a general form of the alternative hypothesis of a chi-square test? Variables A and B are not associated. Variable A influences variable B. Variables A and B are not dependent. Variables A and B are not independent.
3. Four blood types O, A, B and AB occur in the population with frequencies 0.45, 0.4, 0.1, and 0.05 respectively. Within all the blood types, the Rh factors, plus and minus, occur with frequencies 0.85 and 0.15 respectively. Find the probability that a randomly selected person has: (a) type A…
Match the graph to the description that best fits. Use each only once. Symmetric 30+ 25+ Skewed right 20- 15 a. 10 Skewed left Bimodal 30+ 25+ 20 15 b. 10- c. of 230 235 2015 d. 10 5 Q σ Q Q
Question 12 4 pts A study is done to look at the cost of a hotel room in Paris and a hotel room in London. The mean cost in Paris was \$534.50 per night and in London \$369.50. The 95% confidence interval for cost in Paris is (\$437, \$632) and the 95% confidence interval for the cost in London…
3 Problem set for Section 3.3 Binomial Distributions 1. For the following experiments, determine if the trial results in a binomial distribution. If so, specify the parameters p and n. If not, briefly explain how the model fails to meet a condition of binomial distributions. (a) Surveying 12…
x (x - x) (x - x)^2 x x^2 6 11 14 17 18 6
3. Find a single-sampling plan for which p1 = 0.05, a = 0.05, p2 = 0.15, and b = 0.10.
Which confidence interval would lead you to Fail to Reject Ho? Test value: 10 Confidence Interval: 13.1 - 15.1 Test value: 10 Confidence Interval: 9.2 - 9.8 Test value: 5 Confidence Interval: 5.6 - 6.9 Test value: 5 Confidence Interval: 4.5 - 6.3
7. Suppose annual snowfall in Big Bear City is normally distributed with mean average of 58 inches ($\mu$ = 58) and standard deviation of 10 inches ($\sigma$ = 10). What's the probability that a randomly selected year has more than 70 inches of snowfall? P (x ≥ 70) (6 pts) -1E99 μ 1E99 8. Test…
I see restriction of range here. A. yes B. no NEO Ezscore 300 S. Oishi et al./Journal of Research in Personality 58 (2015) 55-68 20000 25000 Elevation Difference r=-.40, p<.01 Fig. 1. The inversion between elevation difference (Highest Point Lowest Point) and extraversion in Study 3. Chapter 8…
1. Calculate the mean, median and standard deviation of the following data .29 .104 .207 .145 .105 .124 All work should be done by hand, cannot use any software, only use calculator
A student from the economics department conducted a study to identify the percentage of family income allocated to the purchase of groceries. She surveyed a random sample of 60 families and compiled the following numeric frequency distribution: Percentage family income Number of families 10-20%…
Problem 1: A random variable X whose probability density function is given by $$f_x(x) = 0.38\delta(x-2) + k \text{tri} \left(\frac{x-2}{3}\right).$$ Another random variable Y is related to X through Y = 2X-3. Find 1. The value of k 2. The expected value and the variance of X 3. The probability…
Let the joint MGF of (X,Y) be: $$M(s,t) = e^{10s + 6t + 32s^2 + 2t^2 + 8st}$$ Then the distribution of X|Y = 7 is:
patients who had little or no evidence of retinopathy at baseline. Retinopa-thies are abnormalities of the retina that sometimes occur among diabetic patients and can result in substantial losses of vision in advanced stages. Patients were randomized to either Sorbinil, an aldose-reductase…
The random variable X is distributed exponentially with mean 1. Find the pdf of Y = (X – 1)².
Question 7 (1 point) Listen Which of the following are criteria for the One-Way ANOVA test? the samples must be independent the populations must be normally distributed the populations must have the same variance n≥ 30 for each sample np(1-p) ≥ 10 for each sample
If X = 131, σ = 26, and n = 33, construct a 95% confidence interval estimate of the population mean, μ. με (Round to two decimal places as needed.)
21. In the following regression, write the auxiliary regression used in the White test for heteroskedasticity: $$y_t = \beta_0 + \beta_1 x_{1t} + \beta_2 x_{2t} + u_t$$ 22. What is the null and alternative hypothesis of the White test of heteroskedas- ticity? 23. If the p-value of the F-test in…
Problem 4.1: (20 points): Statistics Suppose that the data given below were measured in an experiment. 15, 16, 5, 7, 20, 19, 8, 13, 6, 17, 6, 9, 19, 6, 14, 8, 20, 5, 18, 8, 13, 7, 18 a) (6 pts.) Construct a frequency table if the class width is 3. b) (6 pts.) Use the frequency table to draw a…
Use the t-distribution to find a confidence interval for a difference in means µ₁ – μ₂ given the relevant sample results. Give the best estimate for μ₁ - µ₂, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately…
4.195 Traffic Fatalities. According to Accident Facts, published by the National Safety Council, a probability distribution of age group for drivers at fault in fatal crashes is as follows. Age (yr) Probability 16-24 0.255 25-34 0.238 35-64 0.393 65 & over 0.114 Of three fatal automobile…
Data was collected on the dear population in Oregon for the last ten years. Reference the graph below to determine the initial amount of deer counted in the population. N(t) 320- 300- 280- 260- 240- 220- 200- 180 (6, 180) 160 140 120 100 80 Deer Population 0 1 2 3 4 5 6 7 8 9 10 Years t
Let $X_1$, $X_2$, ..., $X_n$ be IID random variables, where $X_i$ ~ Uniform (0, 1). Define the sample mean as $M_n = \frac{X_1 + X_2 + ... + X_n}{n}$ Use Chebyshev's inequality to find an upper bound on $Pr[|M_n - \frac{1}{2}| \geq \frac{1}{100}] \leq \frac{C}{n}$ Give the value of C correct to…
Mr. Ratajski wants to analyze his student's performance in Algebra II Accelerated for his students for the first semester. The semester one grade for his class are listed below: 86 78 72 89 81 85 40 93 80 76 79 88 92 94 44 90 92 78 65 68 79 85 90 88 99 94 a) Organize the numbers above in order…
6. Given Z is the standard normal variable, find a) P(|Z| > 1.75), b) P(|Z| < 2.05).
Question 3 A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of…
Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .179 .032 .026 2.023 a. Predictors: (Constant), AGE Model Sum of Squares df Mean Square F Sig. 1 Regression 23.784 1 23.784 5.812 .0175 Residual 720.238 176 4.092 Total 744.022 177 a. Dependent Variable: INCOME b.…
23. The nicotine content in milligrams (mg) in cigarettes of a certain brand is normally distributed with mean $\mu$ and standard deviation $\sigma = 0.1$mg. The brand advertises that the mean nicotine content of its cigarettes is 1.5 mg, but measurements on a random sample of 100 cigarettes of…
3) Complete the diagram below to determine the percentage of each portion of the normal distribution. Use the Empirical Rule to help you determine each portion. IT -3σ -2σ -σ μ +σ +2σ +3σ 68% 95% 99.7% 4) In a random selection of 50 freshman, each student's height (in inches) is measured and…
12. An ice-cream store has 31 flavours of ice cream and three types of cones (waffle, sugar, and plain). a) Determine the number of possible single-scoop ice-cream cones. b) How many two-scoop ice-cream cones are possible if waffle-chocolate- strawberry is considered different…
As a promotional gimmick, OHaganBooks.com has been selling copies of Encyclopædia Galactica at an extremely low price that is changed each week at random in a nationally televised drawing. The following table gives the frequency with which each price will be chosen and summarizes the…
Exhibit 14-6 You are given the following information about x and y. X Independent Variable y Dependent Variable 4 12 6 3 2 7 4 6 Refer to Exhibit 14-6. The sample correlation coefficient equals a. -.1905 b. .4364 c. .1905 d. -.4364
Question 3 (1 point) The greatest number that can belong to the class Class boundaries Lower class limit Class width Upper class limit
Thirty-four percent of US residents have blood type A-positive. If a random sample of 5 US residents is chosen, find the probability that at most one if the sample has A- positive blood type. .068 .323 .200 .448 .677
60 20 40 60 80 20 0 680 20 40 60 20 0 60 80 60 440 20 0 20 40 60 80 100 0 20 40 60 80 100 C 0 20 40 60 80 100 0 20 40 60 60 D 0 20 40 60 80 100 Which scatterplot has a correlation coefficient of 0.99? Scatterplot A Scatterplot B Scatterplot C Scatterplot D
2.2 The following data sample were obtained from student class test for statistical module. The number of students were grouped in the range of their test mark as in the table below: Range of marks in % Number of students 0-10 6 10-20 8 20-30 16 30-40 9 40-50 15 50-60 33 60-70 19 70-80 6 80-90…
Exercise 03.25 Algo (Measures of Variability) Question 4 of 8 Hint(s) Check My Work Consider a sample with data values of 26, 25, 20, 15, 32, 33, 29, and 25. Compute the range, interquartile range, variance, and standard deviation. Round to 2 decimals, if necessary. Range 18 Interquartile…
26. ______ test is not an appropriate test to examine the group difference with a continuous DV. O ANOVA O Dependent-Sample t-Test O Chi-square O Independent-Sample t-Test
2) An m&m fan is munching on some m&m's surfing the web when they come upon a site. According to the site, 24% of m&m's are blue, 20% are orange, 16% are green, 14% are yellow, 13% are red, and 13% are brown. They want to check if this is false. They take a bag containing several m&ms and finds…
84.6% of the times to prepare an order vary from the regression line by less than 1 hour. 95% of the times to prepare an order can be predicted accurately based on the dollar amount of the order. 84.6% of the variation in the times to prepare an order is due to factors other than the dollar…
Internet Local Men 256 543 799 Women 212 108 320 468 651 1119 16. Use the given table (above) of shopping data by modality and gender to find the indicated probabilities. a. When making a single selection find P(Internet or Men) a) 0.800 b) 0.903 c) 0.811 d) 0.798 e) None of the above b. When…
21) The p-value is 1.2 Points the same as the z statistic. a sample statistic a distance a probability
The categories, or grouping of data, collected for a specific measure are known as ______. a. variables b. attributes c. criterion d. reasoning
Quest 1260, 1446, 1106, 1269, 1443, 1424, 1118, 1132, 1177, 1115, 1156, 1262, 1215, 1236, 1243, 1169, 1437, 1191, 1401, 1439, 1365 Price of Refrigerators (in Dollars) Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative…
Percentage family income Number of families 10-20% 6 20-30% 14 30-40% 16 40-50% 12 50-60% 4 60-70% 8 a. Compute and interpret the (approximate) mean percentage of family income allocated to grocery purchase. (10)
Suppose you work for a smoothie shop and you want to assess whether the average transaction value at your shop is different from the competing smoothie shop on the other block. To do so, you randomly sample 19 of your shop's transactions and record a sample average of $9.75 and sample…
Practice: The Mean and Variance of Binomial Distribution 2 puntos posibles (calificados) Recall that the pmf of a Binomial distribution Binom (n, p), with known n can be written as: $$f_0(y) = exp\left(\frac{y\theta - b(\theta)}{\phi} + c(y, \phi)\right).$$ Refer to the answer of b (0) and $ to…
Problem 4. (25%) Let X and Y be independent random variables with common probability density function, in other words $$f_X(x) = \begin{cases} \exp(-x) & \text{if } x > 0 \\ 0 & \text{elsewhere} \end{cases}$$ $$f_Y(y) = \begin{cases} \exp(-y) & \text{if } y > 0 \\ 0 &…
6 The specifications for a certain type of surveillance system state that the system will function for more than 12,000 hours with probability of at least .90. Fifty such systems were checked and eight were found to have failed before 12,000 hours. These sample results cast some doubt on the…
1. In 2023, Southwest Airlines had 76% On-Time Percentage (OTP) for flights. Suppose 4 flights are randomly selected from Southwest Airlines, find the probability of each: a) All four are On-time (x = 4). b) None of the four are On-time (x = 0). c) At least one is On-time (x > 1). 2. Fantasy 5…
Question 1 A study of soft drink and smoking habits was conducted. Of 12,580 people who said they consume soft drinks weekly, 2694 said they were smokers. Of 14,873 who said they almost never consume soft drinks, 2497 were smokers. To find the point estimate to construct a confidence interval…
Suppose that $X_1$, $X_2$, ..., $X_n$ and $Y_1$, $Y_2$, ..., $Y_n$ are independent random samples from populations with means $\mu_1$ and $\mu_2$ and variances $\sigma_1^2$ and $\sigma_2^2$, respectively. $$U_n = \frac{(\overline{X} - \overline{Y}) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2 +…
For a normal variable X ~ N(μ = 27.3, σ = 5.7), find the probability P(28.35 < X < 29.15): P(28.35 < X < 29.15) = (Round the answer to 4 decimal places) Question Help: Video 1 Video 2 Video 3 Written Example 1 ☑ Message instructor Check Answer Jump to Answer Question 2 0/1 pt3 Details For a…
Group Statistics Fertilizer N Mean Std. Deviation Std. Error Mean Growth One 12 14.25 Two 12 13.08 4.181 4.660 1.207 1.345 Growth Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances Independent Samples…
MAT 102 703- Liberal Arts Math Test: Final Exam Question 7 of 12 The accompanying table gives the number of copies sold for 30 top-selling novels. Use data given in the table to construct a frequency distribution with a first class (in millions) of 50-99. samantha sanchez 05/14/24 7:42 PM This…
The diameters of metallic spherical engine components is a continuous random variable and is uniformly distributed between $$1.4 < X < 2.6$$ a) Determine the cumulative distribution function of the diameter. [5 points] b) Determine the proportion of diameters that exceed 2.1 millimeters. [6…
Consider the following exponential probability density function. $$f(x) = \frac{1}{2}e^{-x/2}$$ for $x \ge 0$ If needed, round your answer to four decimal digits. (a) Choose the correct formula for $P(x \le x_0)$. (i) $P(x \le x_0) = 1 + e^{x_0/2}$ (ii) $P(x \le x_0) = 1 - e^{x_0/2}$ (iii) $P(x…
Linear Combination of RVs Ex: Let Y = X₁ - X2 and assume a joint density function of two RVs X1 and X2 is given by $$f(x_1, x_2) = \begin{cases} 3x_1 & 0 \le x_2 \le x_1 \le 1 \\ 0 & \text{elsewhere} \end{cases}$$ Find the mean and variance of Y.
1. The joint pmf of two random variables X and Y is given by $$P_{X,Y}(x,y) = \begin{cases} c(x+y) & x = 1,2; y = 1,2,3 \\ 0 & \text{elsewhere} \end{cases}$$ (a) Find the constant c. (b) Find the marginal pmf of X and of Y. (c) Find the probability P[Y > X].
Question 4: The mean lifdetime of a sample of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation Of 120 hours. a) Test the hypothesis that the mean lifetime is at most 1600 hours. (probability of type I error =0.05). b) How large a sample of…
Problem 1 (25%) due 05-16-2024 A wire manufacturing company has inspectors to examine the wire for fractures as it comes out of a machine. The number of fractures is distributed in accordance with a Poisson process, having one fracture on the average for every 50 meters of wire. One day an…
7) Parameters are 1.2 Points numerical characteristics of a sample. numerical characteristics of a population the averages taken from a sample. numerical characteristics of either a sample or a population.
Which of the following statements is TRUE regarding older adults and fluid intake. Older adults require the same amount of fluids as younger adults. Older adults typically drink the recommended amounts of fluids. Older adults require less fluids than younger adults. Older adults require more…
5). Assume X, Y are independent random variables. X satisfies normal distribution with mean 0 and variance 4; Y satisfies normal distribution with mean 5 and variance 9. i. What is the distribution of X²? ii. What is the distribution of 3X? iii. What is the distribution of -4Y? iv. What is the…
4. a) Three parts are assembled in series so that their critical dimensions $x_1$, $x_2$ and $x_3$ add. The dimensions of each part are normally distributed with the following parameters: $\mu_1$ = 55, $\sigma_1$ = 2, $\mu_2$ = 65, $\sigma_2$ = 3 and $\mu_3$ = 92, $\sigma_3$ = 3. If the…
The lengths of pregnancies in a small rural village are normally distributed with a mean of 269 days and a standard deviation of 12 days. 15.[2] In what range would you expect to find the middle 50% of most pregnancies? Round your answer to the nearest tenth of a day. 16.[3] If you were to draw…
If the universal set U={0,1,2,3,4,5,6,7,9,11) has two subsets A={1,3,5,11} and B={0,2,3,9,11). Find: BUA A Question 6 (3 points) Listen Find the probability of the given event occurring: Receiving either a first or a second prize in a drawing involving 3 other people. In the first text box,…
What is the value of ?(X - 4)^2 for the following scores? Scores: 4, 1, 6, 5 62 74 14 0
Contingency Table Type of Heating By Delinquent in Payment? Count Yes No Totals Electricity 20 130 150 Heating Oil 15 20 35 Natural Gas 50 240 290 Propane 12 39 51 Totals 97 429 526 Use the JMP output below to report the correct p-value degrees of freedom and the ? Report the numbers as listed…
1) Lastik materyallerin testi için yapılan bir deneyde lastik yapımında kullanılan A katkı maddesi oranı ve materyal kalınlığı etken olarak alınmıştır. Araştırmada bağımlı değişken 10 kilogramlık bir ağırlığı yerden bir metre yukarı kaldırmak için geçen süre olarak belirleniyor. Katkı maddesi…
The lives of all televisions manufactured by the Lucky Goldstar ("LG") company has a normal distribution with a mean of 60 months and a standard deviation of 12 months. LG provides a replacement warranty - all television found to be defective in the first two years, the company will replace…
1. Four catalysts that may affect the concentration of one component in a three- component liquid mixture are being investigated. The following concentrations are obtained from a completely randomized experiment: Catalyst Observations…
20) Compute the probability of X successes. n = 4, X = 3, p = 0.1 ID: BESB8e 5.3.4-1
Suppose you work for a smoothie shop-and you want to assess whether the average transaction value at your shop is different from the competing smoothie shop on the other block. To do so, you randomly sample 19 of your shop's transactions and record a sample average of $9.75 and sample standard…
11. In a randomized control trial for Calorie-Reduction (CR), 27 participants had a sample mean weight loss of x = 5.42 kg and standard deviation of s = 9.39 kg. What is the 95% confidence interval (CI) and margin of error (ME) for the population weight loss, u, of all participants on…
01. (2p) 50 Samples of a part of 3D-printer are classified as shown in the table below on the basis of conformity to Depth and Width specifications The number of parts which conform to Depth Specifications Yes No The number of parts which conform to Width…
At least 12% of car crashes occur within 2 miles of the motorists home. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage). $H_0: p$ $H_1: p$ Use the following codes to enter the following symbols: $\geq$ enter $\ge$ $\leq$ enter $\le$ $\neq$…
Let Y denote a random variable that has a Poisson distribution with mean λ = 3. (Round your answers to three decimal places.) (a) Find P(Y = 5). (b) Find P(Y ≥ 5). (c) Find P(Y < 5).
1) Mr. Ratajski wants to analyze his student's performance in Algebra II Accelerated for his students for the first semester. The semester one grade for his class are listed below: 80 78 72 89 81 85 40 93 80 75 79 88 92 94 44 90 82 78 65 68 79 85 90 88 99 94 a) Organize the numbers above in…
[ ] 17. [10=2+8 pts] According to the American Red Cross, 7% of people in the United States have blood type O-negative. A simple random sample of 300 Americans is selected and it is determined whether each person in the sample has O-negative blood type. a) Verify the condition that allows us to…
In hypothesis testing, in order to reject the null, our P value (P) must be ______ our preset Alpha (a) Value. O greater than less than O equal to O in opposition to
Imports and Exports A random sample of countries shows the value of U.S. exports and the U.S. imports for each country for a recent year. The data are in hundreds of millions of dollars. Assume the independent variable is…
In a standard Normal distribution, if the area to the left of a z-score is about 0.5712, what is the approximate z-score? Click here to view page 1 of the Standard Normal Table. Click here to view page 2 of the Standard Normal Table. z= (Round to two decimal places as needed.) Area under the…
There is no independent valid test for ADHD. True False There is no independent valid test for ADHD. True False
NAME: SCORE: Decimal Averages Independent Practice INSTRUCTIONS: Find the averages for each set of data. Round answers to the nearest hundredth 1. 10.2, 2.17, 5.67, 11.70, 0.72 2. 97.87, 78.25, 7.80, 34.27, 40.42 3. 10.51, 1.44, 39.32, 64.09, 27.38, 50.66, 76.37 4. 65.81, 26.96, 64.24, 1.79,…
1(b) The graph below has several tables representing the probability distribution (CO1) values of the given 5 variables. $e^0$ 0.7 $e^1$ 0.3 Exam level IQ level $i^0$ 0.8 $i^1$ 0.2 $i^0$, $e^0$ $m^0$ 0.6 $m^1$ 0.4 Marks Apti. score $i^0$, $e^1$ 0.9 0.1 $i^1$, $e^0$ 0.5 0.5 $i^1$,…
4. Randi commutes to work in a very high traffic area. There is a 95% chance that she hits a red or amber light during her morning drive. What is the expected number of drives before Randi has a drive with no red or amber lights? (3 marks)
1. A Social Science student conducted a study to assess the association between two variables measured at a categorical level for Creativity and Online gaming activities among adolescents. The following data were obtained. Online gaming activities Low Moderate High Above average…
2 Problem set for Section 5.2 Expectation 1. Let X have the discrete uniform distribution on 7 letters (meaning, it models rolling a balanced 7-sided die). 1 (a) Calculate the mean μ (b) Calculate the standard deviation σ 2. When you give a casino $5 for a bet on the "pass line" in a casino…
Question 2: In another part of the paper, they look at the characteristics of people who were classified as 'low' or 'moderate' chocolate consumers. Total daily chocolate consumption Low (<= 10 g/day) Moderate (> 10g/day) Total Men 19 34 53 Women 29 49 78 Total 48 83 131 a) What would be an…
D Question 20 1 pts A factor is considered a confounder if that factor is a known risk factor for a disease of interest and if that factor is associated with an exposure of interest. (mark True or False)
A large school district receives funding to assess the effectiveness of a new reading curriculum. They have enough money to test the curriculum with a large sample of students within the district. Briefly explain which type of participant sampling (probability or non-probability) is more ideal…
3. (15 pts.) Un fabricante de equipo deportivo desarrolló un nuevo sedal para pesca sintético que, según afirma, tiene una resistencia media a la rotura de 8 kilogramos con una desviación estándar de 0.5 kilogramos. Pruebe la hipótesis de que µ = 8 kilogramos contra la alternativa de que µ ≠ 8…
Find the value of the linear correlation coefficient r. x 57 53 59 61 53 56 60 y 156 164 163 177 159 175 151 (1 point) Ο 0.109 -0.054 Ο 0.214 Ο -0.078
b) The number of roses and the number of lily flowers are noted every week at a garden during an observation. The observation readings of 4 successive weeks are as follows: Compute the coefficient of determination and interpret the result. (7 marks) Rose Lily 2 4 3 1 6 2 5 3 $$r = \frac{n(\sum…
7. (13 points) CSUN Statistics department purchased 24 Dell laptops from a dealer in order to have a supply on hand for tests for use by students who forget to bring their own. Although the department was not aware of this, five of the laptops were defective. When a test is being written,…
2. A linear probability model (LPM) has been estimated using Ordinary Least Squares (OLS) with a sample of N = 500 observations, yielding the following results: Y = 12.4 + 3.4X1,i – 0.2X2,i + ûi (23) (3.2) (-0.9) Knowing that the values in parentheses correspond to the individual significance…
2. The random variable X has the following probability density function: $$f(x) = \frac{2}{\lambda^2}xe^{-x^2/\lambda^2}, x \ge 0$$ where $\lambda$ is a positive parameter. (15 points) (a) It can be shown that $$E(X) = \frac{\sqrt{\pi \lambda}}{2}$$ and $$E(X^2) = \lambda^2$$ Set up (but do not…
Determine the level of measurement of the variable. Ages of children: 5 years, 6 years, 7 years, 8 years, and 9 years Choose the correct answer below. Ratio Nominal Interval Ordinal
Problem 4.4 (20 points): Continuous RV The cumulative distribution function of random variable X is $$F_x(x) = \begin{cases} 0, & x<-1 \\ \frac{(x+1)}{2}, & -1\leq x<1 \\ 1, & x\geq 1 \end{cases}$$ a) What is the probability P[X > 1/2]? b) What is the probability that P[-1/2 ≤ X <3/4]? c) What…
State Prison Dollars Violent Crime per Capita (x) Rate (y) Iowa 150 6.57 Idaho 51 2.23 Maine 199 4.20 Nebraska 55 2.81 Tennessee 179 6.91 N=5
9. In 2023, FICO scores a mean of 715 (μ = 715) and a standard deviation of 42 (σ = 42). a) Find P95, the 95th percentile, the score that separates the bottom 95% from the top 5%. 0% 50% 100% b) Find P99, the 99th percentile, the score that separates the bottom 99% from the top…
Question 42 0.2 pts Lung cancer is the leading cause of cancer-related deaths in the United States. Researchers are interested in studying the relationship between aspirin use and lung cancer - for example, whether the use of aspirin reduces the risk of lung cancer. To study this, they…
Participants in a study investigating the relationship between coffee consumption and exercise were asked to report the number of steps per day they completed over the past week. The table below gives summary statistics for the daily step count of study participants based on the amount of…
Pregnant Woman Before Treatment After Treatment Difference Sign 1 8 3 2 10 7 3 6 5 4 8 10 5 11 10 6 8 2
Suppose the X is a continuous random variable whose probability density function is given by $$ f(x) = \begin{cases} kx, & 0 \le x < 3, \\ 2 - \frac{x}{2}, & 3 \le x \le 4, \\ 0, & \text{otherwise} \end{cases} $$ (a) What is the value of k? (b) What is the cumulative distribution function of X,…
$f(y) = (\theta + 1)y^\theta$, $0 < y < 1$, $\theta > -1$. (a) Derive the maximum likelihood estimator of $\theta$. Show all working.
An instructor wants to use two exams in her classes next year. This year, she gives both exams to the students. She wants to know if the exams are equally difficult and wants to check this by looking at the differences between scores. If the mean difference between scores for students is "close…
In a normal distribution, what z- score cuts off the top 15% of the distribution? z = -0.91 z = -1.04 z = +0.91 z = +1.04
4. (15 pts) Consider a coin. Assume that, when we toss it once, the probabilities on the outcomes H, T are given by P({H}) = p and P({T}) = q, where p, q > 0 and p + q = 1. Now, we toss the coin three times and asume that one or two tossings does not affect the rest. Consider the following…
MLE for Poisson distribution Calculate likelihood function $$L(\lambda) = \prod_{i=1}^m P(x_i | \lambda)$$ $$L(\lambda) = \prod_{i=1}^m \frac{e^{-\lambda} \lambda^{x_i}}{x_i!}$$
19. An instructor gives a test before and after a tutoring session and results from randomly selected students are given here. Test the claim that the tutoring improved scores. Before 64 51 67 87 51 67 34 71 81 After 70 56 64 89 51 77 42 71 90 a. Find the P-value b. Will the null hypothesis be…
A marketing team needs to complete a marketing campaign project which involves six activities. The network diagram for the project is presented below. A B Start End C D E F The team has the following partially completed estimates of means and standard deviations. Some are at the activity level,…
Let x be the number of successes observed in a sample of n = 6 items selected from a population of N = 12. Suppose that of the N = 12 items, M = 7 are considered "successes." Find the probability. (Round your answer to four decimal places.) the probability of observing at most two successes You…
Find the sample size needed if a 98% confidence interval has a 'margin of error' of 4% if ... You feel safe using an estimate for p of .13 You are going to play it as safe as possible and use p of .50 Find the sample size needed if a 99.8% confidence interval has a 'margin of error' of 0.5%…
Problem 3 (25%) The joint probability mass function p(x, y) of the random variables X and Y is given by the following table. Find the conditional probably $P_{X|Y}(x|y)$ for all possible pair of (x,y). You can list all the probability as a table with format similar to the following…
Which of the following correctly describes the formula for the p-value in the mammography study, given an observation of $Y = 39$ deaths due to breast cancer in the treatment group of 31000? $P_{H_0}(T \le 39)$, the probability under $H_0$ to obtain the observed value or a more extreme value of…
6. $X_1, X_2, ..., X_n$ are a random sample from $N(\mu, 1)$. (a) Find the Cramér-Rao lower bound of the variance of unbiased estimators of $\mu$. (b) Show that the sample mean is the MVUE using (a).
Duration of the test: 60 mins. Only pocket calculator and the Formulas down any particular results. Signature 1. Suppose that we have a sample space with five equally likely elementary outcomes: E1; E2; E3; E4; Es Let A= { E1; E2} B={ E4;E5) a) Find P(A), P(B), P(C) b) Find P (AOC). c) Find…
Control group Exposure group 3 9 6 6 3 4 4 5 3 4 1 3 2 4 5 4 7 6 8 7 8 a. Test for hypothesis at a significant level of 0.05 if there is a difference between the two groups with regard to statistics anxiety levels. Show all your calculations and hypothesis-testing steps. (16 marks). b.…
A statistics professor randomly selects 20 of her students and records their final exam scores. 89 15 67 84 14 78 59 45 85 67 96 15 23 46 19 84 17 39 24 83 Find the percentile for 24. Find $P_{83}$ (the value that corresponds to the 83rd percentile). 65 84 Done
You wish to test the following claim ($H_a$) at a significance level of $\alpha = 0.01$. $H_o: \mu = 57.1$ $H_a: \mu \neq 57.1$ You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size $n = 16$ with mean $M = 44.5$ and a…
e. What is your decision regarding $H_o$? What is your decision regarding $H_o$? Do not reject There is insufficient evidence to conclude that the population mean is greater than 20.
Kuhn and Pease (2006) compared hypothesis-testing skills of 11- to 12-year-olds with those of young adults. They were asked to choose accessories for a charity giveaway, then were given data based on their selections. To use the data most effectively, participants needed to attend to their…
Example If {Yt} is from the following model Yt = 0.5 Yt-1 + 0.2 Yt-2 + Et - Et-1 Et ~WN(0.1). (1) Express Yt = FYt-1 + Vt. Vt = [Ut] 0 Ut = Et - Et-1 (2) Is {Yt} stationary (check the eigenvalues of F) (3) Express Yt = Et + Y1 Et-1 + Y2 Et-2 + ... Give Y1 value. (4) Write the relations…
Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that less than 15% of firms in the manufacturing sector provide child-care benefits to their workers. A random sample of 350 manufacturing firms is selected and asked if they offer…
2. What is power of a test? Select all that applies. ✔1-P(type II error) PHA (reject Ho) 1-P(type I error) PHo (reject Ho) x
A salesman has 8 presentations scheduled for the coming month. Historically, 30% of her presentations have resulted in sales. It is reasonable to assume that her chance of making a sale in any given presentation is not affected by what happens in any other presentation. Find the following…
At a recent company picnic with over 2000 guests, an outbreak of food poisoning occurred. A doctor suspects that the potato salad may be related to the food poisoning. A random sample of 200 guests asked about their symptoms and whether or not they ate the potato salad. The data is presented in…
Let z be a standard normal random variable with mean ? = 0 and standard deviation ? = 1. Find the value c that satisfies the inequality. (Round your answer to two decimal places.) P(z > c) = 0.0233 c = You may need to use the appropriate appendix table to answer this question.
a-1. Construct a contingency table that cross-classifies the data by Age and Brand. Provide the frequencies in the accompanying table. Brand Age A B C ≥ 35 years old (0) < 35 years old (1) a-2. How many of the purchases were for Brand A? Number of purchases for Brand A a-3. How many of the…
Four hundred draws are made at random with replacement from a box. The average of the draws is 28.5 and the SD is 20. Someone claims that the average of the box equals 26.5. Is this plausible? Find P and decide whether the average of the box equals 26.5 or is more than 26.5. Selected Answer: P…
1 Please round Pi to three decimal places. 3 2 Find the absolute value of -22. Important Functions 3 Generate a random number between 0 and 1 and display it in percentage (for example, 99.99%). 5 4 Generate a random number between 1 and 100. 65 What is 15 squared? 7 6 What is 8 cubed? 8 7 What…
2. Suppose you are modeling the number of accidents occurring at a particular intersection each month. Which distribution would you use for this scenario? Justify your choice. (5 pts)
Answer the question for a normal random variable x with mean μ and standard deviation σ specified below. (Round your answer to four decimal places.) μ = 1.3 and σ = 0.18. Find P(1.00 < x < 1.10). USE SALT P(1.00 < x < 1.10) = You may need to use the appropriate appendix table to answer this…
Scenario 1 (Part A): Dr. Ramirez investigated the association between college students' anxiety symptoms and help seeking behaviors. She used a subset of items from the Anxiety Symptoms Questionnaire (ASQ) to assess the frequency of anxiety symptoms. She used a new survey she created to assess…
3. A certain characteristic is said to be related with the eye colour. A sample of 160 randomly selected individuals are obtained and the results are tabled below: Has characteristic? Yes No Eye colours Brown Blue Others 20 35 15 35 25 30 Let R denotes the event that a selected individual has…
Question 1 Which source of bias is most relevant to the following situation: The CEO of a company asks employees to call an anonymous phone-line to report concerns about their work environment. self-interest study voluntary response bias nonresponse bias or missing data perceived lack of…
Before revealing your final exam grades, your instructor tells you that there is a linear relationship and a correlation of 0.7 between the exam 2 grades and the final exam grades. The average grade on exam 2 was 86 and the average grade on the final was 91. The standard deviation on exam 2 was…
1. In the linear probability model (LPM): a. The model parameters can be estimated consistently and efficiently using the method of Ordinary Least Squares (OLS) estimation. b. The dependent variable can't take discrete values, Y = 0 and Y = 1. c. The error term of the model is…
A researcher was interested the relationship between fetal heart beat rate at 7 weeks gestation and healthy Apgar scores 5-minutes after full-term birth (a measure of how well the infant is doing after birth). Healthy fetal heart rates at 7 weeks range from 110-160 bpm. Apgar ratings of 7 or…
Find the normalizing constant of the pdf satisfying $$f(x) \propto xe^{-x^2} 1(x>0).$$
Caffeine in Tea Bags In a recent study, researchers found that the average amount of caffeine in tea bags is 26 mg. The standard deviation of the population is 3 mg. If a random sample of 45 newly manufactured tea bags has a mean of 24.8 mg of caffeine, can it be concluded that the new brand of…
17. Describe how the mean compares to the median when a distribution is skewed to the right. OA. Mean > median OB. Mean < median C. Mean = median OD. Both mean and median = 0
A builder claims that heat pumps are installed in more than 70% of all homes being constructed today in a city. Test this claim at the 10% significance level if a survey showed that 11 out of 15 homes had heat pumps installed. (A) State the null and alternate hypotheses. (2 points) (B) What is…
6 The random variable X is distributed normally with a mean of 300 and a standard deviation of 5. Find the following: a P(X > 305) b P(X < 291) (AC 4.2) C P(X < 312) d P(X > 286)
Use the following data set and conduct a two-talled test of significance using the Pearson r. Use alpha = .05. Label your answers. A. What are your null and alternative statistical hypotheses for this correlation? B. What are your degrees of freedom AND what is the critical value? C. Calculate…
Provide an appropriate response. Find the equation of the regression line for the given data. Round values to the nearest thousandth. -5-341-1-20 X y -10-89 v=2.097x-0.552 023-4 1-2-6-13 6-8 = 0.522x - 2.097 =-0.552x + 2.097 y = 2.097x + 0.552 0000
El siguiente ejercicio es ficticio. Un veterinario le inyectó 10 mg del antibiótico gentamicina (por cada kilogramo de peso corporal) a cinco ovejas hembra sanas de tres años. Las concentraciones de gentamicina en la sangre de estas ovejas, luego de una hora y media (en µg/ml), fueron las…
Evaluate the expression.\ $frac{sqrt{15}}{sqrt{8}}$\ $frac{sqrt{15}}{sqrt{8}} approx oxed{}$ \ (Do not round until the final answer. Then round to two decimal places as needed.)
Question 7 1 pts What is the mode on the graph below? 12 10 8 6 4 2 0 1 2 3 4 5 6 7 7 Two modes: 11 & 9 Two modes: 6 & 7 No mode
1. Prove the following properties of covariance: • cov(X, Y) = cov(Y, X) • cov(X,X) = Var(X) (15 pts) • cov(aX, Y) = a cov(X, Y) for any constant a • cov(X+c, Y+d) = cov(X,Y) where c and d are constants
Let X(t) be a continuous-time random process defined by X(t) = Acos(ωt+Φ) where the random variables A ~ Uniform (0,1) and Φ ~ Uniform (0,2π) are independent. The autocovariance function of the process X(t), Cx(t, t_0), is given by 0 1/6 cos(ω(t_1 - t_0)) 0 1/4 cos(ω(t_1 - t_0)) 0 1/3 cos(ω(t_1…
4.5.11. Let $Y_1 < Y_2 < Y_3$ be the order statistics of a random sample of size $n = 3$ from a distribution with pdf $f(x; \theta) = 1/\theta$, $0 < x < \theta$, zero elsewhere, where $0 < \theta$. The hypothesis $H_0: \theta = 1$ is rejected and $H_1: \theta > 1$ is accepted if the observed…
We perform a two-tailed hypothesis test on the population correlation coefficient between movie goers' snack spending and their age, at a = 0.05. For this, we collect a sample of 25 moviegoer's age and snack spending and the sample correlation coefficient r = -0.373. a. [2pts] Specify both the…
1. A Social Science student conducted a study to assess the association between two variables measured at a categorical level for Creativity and Online gaming activities among adolescents. The following data were obtained. Online gaming activities Low Moderate High Above Creativity average…
Estimated Mean 1.525 Hypothesized Mean 1 T Ratio 2.11662 P Value 0.02036 Two sided Low Side High Side Sample Size = 40 In the example above, how many p-values would we be able to reject the null hypothesis for? NOTE - When doing statistical tests, we only choose one alternative hypothesis to…
This study is based on Live-Long, a health shop specializing in natural foods and products. (i) 45% of customers visiting the shop spend more than R 500 on purchases. Consider a random sample of eight customers visiting the shop. (a) Write down four conditions that must be satisfied in order to…
(2pt) Consider a population of size N and simple random sampling (without replacement) with sample size n. Assume that the population takes values {$x_1$, ..., $x_N$} where $x_i$ ∈ {0,1} and that the proportion of 1's satisfies $\frac{1}{N}\sum_{i=1}^N x_i \to p$ as $N \to \infty$ and $p \in…
Question 10, 2.2.22 Part 2 of 8 The data to the right represent the number of customers waiting for a table at 6:00 P.M. for 40 consecutive Saturdays at Bobak's Restaurant. Complete parts (a) through (h) below. OC. The data are continuous because there are a finite or countable number of…
Before experimental drugs can be brought to market, they must undergo many rigorous trials to ensure they deliver their medical benefits effectively and safely. One method that is commonly used in this process is to compare the effects of a drug to that of a neutral placebo in double-blind…
Of the two given p-values, which provides more evidence against Ho? p-value = 0.002 p-value = 0.37
QUESTION 6 In the regression model Y₁ = ẞ0 + B1Xj+B2Di + B3(Xjx Dj) + uj, where X is a continuous variable and D is a binary variable, to test that the two regressions are identical, you must use the: OF-statistic for the joint hypothesis that ẞ2 = 0, β3=0. Ot-statistic separately for ẞ3 =…
In a survey, 1000 adults were asked to identify "what is inappropriate in the workplace." Of the 1000 subjects, 53% said that jeans were not appropriate in the workplace. a. What is 53% of 1000? b. Among the 1000 respondents, 730 said that hats are unacceptable in the workplace. What percentage…
Q9. (a) Let X = (X1 X2 X3)' ~ N3(µ, I) with µ = (2 – 3 1)'. Then obtain the distribution of (i) 3X1 - 2X2 + 5X3 and (ii) (X1-X2 X2-X3). 10
Two of the three conditions for a t-test between means are The samples must be randomly pooled The samples must be randomly selected The samples must be dependent (paired) The samples must be independent
For a population data set, $\sigma = 17.20$. a. What should the sample size be for a 98% confidence interval for $\mu$ to have a margin of error of estimate equal to 6.80? n = b. What should the sample size be for a 95% confidence interval for $\mu$ to have a margin of error of estimate equal…
Bob makes the forecast for the five months of sales. Compared with the actual values of sales for these six months, please compute the mean absolute error (MAE), mean squared error (MSE), and mean absolute percentage error (MAPE). Months January February March April May Actual…
A doctor would like to estimate the mean difference in height of pairs of identical twins. The doctor randomly selects 8 pairs of identical twins and determines the current height, in inches, of each twin. The data are displayed in the table. Pair Twin 1 Twin…
2.1 nomework practice How secure is your Job. A survey of Job Stability was taken below are results. responses very likely Frequency 351 Fairly Likely 403 Not too likely 1872 Not likely 4849 Total ? *please construct a relative frequency balance round answer two decimal places response Very…
1. Selecciona la respuesta correcta (3 ptos). A medida que el tamaño de una muestra de datos continuos aumenta (n→∞), el error estándar de la muestra: a. aumenta (SE → ∞) b. disminuye (SE → 0) c. no cambia Standard Error 2. Selecciona la respuesta correcta (3 ptos). A medida que el tamaño de…
4. Do the following: (a) Suppose that $X_1$, $X_2$ are discrete iid random variables with probability mass function $$p_{X_i}(x) = \begin{cases} 0.4 & x = 0 \\ 0.3 & x = 1 \\ 0.3 & x = 2 \end{cases}$$ i. (6 pts) Compute the joint probability mass function $p_{X_1,X_2}(x_1, x_2)$. ii. (6 pts)…
Suppose that Teddy graphs the temperature and the number of walks he's been hired to shovel. walks shoveled 16 • (-10,14) 14 (0,10) 12 10 (-5,11) (5,8) 8 6 4 (0,7) (20,6) 2 (32,3) -10 0 10 20 30 40 temperature + Calculate the what is the y-intercept (y'=a+bx) for the line of regression.…
56 Out of 500 people sampled, 145 have lied to a family member in the past month. Based on this, construct a 99% confidence interval for the true population proportion of people who have lied to a family member in the past month. Give your answers as decimals, to three places <p<
Problem 2. (25%) Let the joint probability density function of random variables X and Y be given By $f(x, y) = (\frac{2}{9})y * exp(-x)$ if x>0, 0<y<3 f(x,y)= 0 elsewhere Find the marginal probability density functions of X and Y.
In Ms. Tanti's geography class, • 60% of the students are Canadian • 28% of the students are of Chinese origin • 15% are Canadian and of Chinese origin. a) Construct a Venn diagram to represent this information Canadian Chinese b) What is the chance that a student drawn at random would be: i)…
Suppose you work for a smoothie shop and you want to assess whether the average transaction value at your shop is different from the competing smoothie shop on the other block. To do so, you randomly sample 19 of your shop's transactions and record a sample average of $9.75 and sample…
EXAMPLE 3.2 There are four batteries, and one is defective. Two are to be selected at random for use on a particular day. Find the probability that the second battery selected is not defective, given that the first was not defective.
Regression Equation in Uncoded Units Y= 64.375 +3.125 A-0.625 B + 6.875 C-4.375 AB-9.375 A°C+4.375 B°C + 6.62 Ct Pt Question: Use steepest Ascent method to optimize the response. Must show 4 steps for steepest ascent method (Ctpt means center point)
The vapour pressure of water increases with temperature as shown by the formula p = C * e ^ ( - ( ΔvapH^0 ) / ( R * T ) ). The data in the table below shows the vapour pressure of water (in mmHg) at varying absolute temperatures (in…
4. NBA All-Star James Harden has a career Free-Throw percentage (FT%) of 86% (p = .86). In a sample of 50 free-throws (n=50), use the binomial distribution to find each probability: a) Getting exactly 40 FTs (x = 40). (12 pts) b) Getting at most 40 FT (x ≤ 40). c) Getting at most 45 FTs (x ≤…
Compute the range for the set of data. 69, 147, 28, 101, 177 A. 149 B. 104.4 C. 177 D. 28
The null hypothesis of mean profit is 120 SR with population standard deviation = 10. In a sample of n=50 shops, the sample mean is 125 SR. Test the null hypothesis for the alternative hypothesis ≠ 120 SR (use a = 0.05). What is the p- value? nswer:
Twenty students completed statistics course. Each student took a midterm exam and a final exam. Summary statistics of the exam scores are given below. Exam Mean Standard Deviation Midterm 124 50 Final 129 56 In addition, the correlation coefficient equals 0.88. One of the students, Kelly,…
Question 1 [15] Consider the variables listed in 1 to 5 below, that are in a financial report of the Johannesburg stock exchange. Indicate for each of the random variables: (1) the type of the variables if it is a quantitative (numeric), categorical, discrete or continuous; and (2) the…
Complete the following relative frequency table. (Round to the nearest percent as needed.) Relative Relative Frequency Frequency Tar (mg) (Nonfiltered) (Filtered) 2-6 % % 7-11 % % 12-16 % % 17-21 % % 22-26 % % 27-31 % % 32-36 % % Frequency Distributions Tar (mg) in Nonfiltered Tar (mg)…
Considering the following constraints in a linear programming. 3x + y ≤ 50 2x + 3y ≤ 40 x ≤ 15 y ≤ 10 x ≥ 0 y = 0 Question 5 If the objective function is max 6x + 8y, what is the optimal solution for (x,y) with the above constraints? ( ). Rounding to 2-decimal points if needed. 4 pts
1) The Governor of a state has started a program to encourage people to exercise regularly. A concern of critics is that it appears to target women more than men. One year after the program began, a random sample of 800 men and 750 women were selected. Of the men selected, 384 exercise…
Exercise 3.1 - Decide whether or not each statement is necessarily true. 1. If A and B are mutually exclusive events and P(B) > 0, then P(A/B) = 0. 2. I have two dice. Die 1 is a normal die, that is, it has faces and each is obtained with probability. Die 2 is unusual: it has faces, and again…
Question 7 3 pts A researcher studying the proportion of 8 year old children who can ride a bike, found that 319 children can ride a bike out of her random sample of 885. What is the sample proportion? Round to 2 decimal points (e.g. 0.45).
HW Score: 6.25 Points: 0 of Question 2, 3.2.RA-12 Find the population standard deviation for the given data. 9, 16, 30, 35, 40 Select the correct choice below and fill in the answer box to complete your choice. (Round to two decimal places as needed.) A. The standard deviation is s = B. The…
2. The sample mean age of n=20 diabetic patients is 50 years and the sample variance is 100. Find the 99% confidence interval for the population mean age. Answer:
Exercice 11. Let D be the unit disk in R2, D = {(x, y) ∈ R2, x² + y² ≤ 1}. Suppose X and Y have joint pdf f(x, y) = c if (x, y) ∈ D and zero otherwise. (a) Find c. (b) Find the marginal pdf fx and fy. (c) Are X and Y independent? (d) Find E(X) and Var(X). (e) Find the covariance and correlation…
3 1 point Which of the following statements is TRUE about sample size? Sample size is only important in observation research, not experimental research. A large sample size decreases the likelihood that the results of your experiment will be influenced by random Sample size is not that…
Exercise 9.1- Decide whether or not each statement is necessarily true. 1. If X and Y are independent discrete random variables, then $f_{XY}(xy) = f_X(x)$. 2. We repeatedly toss a fair coin. Let U be the number of trials needed to get the first head and V be the number of trials needed to get…
20) 10 pt. Maria has been crossing prize Tea Roses and has created a purple rose by crossing an American Beauty Red with an Amsterdam Black. She suspects that the red and black alleles are incompletely dominant. She shows you the following data obtained from a large number of crosses. Perform a…
Example. The probability that a student passes the written test is 0.7, find the probability that the student will pass the test on the fourth try.
(i) The joint density function of X and Y is given by $$f(x, y) = \begin{cases} 2e^{-x}e^{-2y} & 0 < x < \infty, 0 < y < \infty \\ 0 & otherwise \end{cases}$$ compute: (a) P(X > 1, Y < 1) (b) P(X < Y) (c) P(X < a)
A box contains 50 balls numbered from 1 to 50. If 10 balls are drawn with replacement, what is the probability that at least two of them have the same number? Answer:
Which of the following is a general form of the alternative hypothesis of a chi-square test? Variables A and B are not associated. Variable A influences variable B. Variables A and B are not dependent. Variables A and B are not independent.
3. Four blood types O, A, B and AB occur in the population with frequencies 0.45, 0.4, 0.1, and 0.05 respectively. Within all the blood types, the Rh factors, plus and minus, occur with frequencies 0.85 and 0.15 respectively. Find the probability that a randomly selected person has: (a) type A…
Match the graph to the description that best fits. Use each only once. Symmetric 30+ 25+ Skewed right 20- 15 a. 10 Skewed left Bimodal 30+ 25+ 20 15 b. 10- c. of 230 235 2015 d. 10 5 Q σ Q Q
Question 12 4 pts A study is done to look at the cost of a hotel room in Paris and a hotel room in London. The mean cost in Paris was \$534.50 per night and in London \$369.50. The 95% confidence interval for cost in Paris is (\$437, \$632) and the 95% confidence interval for the cost in London…
3 Problem set for Section 3.3 Binomial Distributions 1. For the following experiments, determine if the trial results in a binomial distribution. If so, specify the parameters p and n. If not, briefly explain how the model fails to meet a condition of binomial distributions. (a) Surveying 12…
x (x - x) (x - x)^2 x x^2 6 11 14 17 18 6
3. Find a single-sampling plan for which p1 = 0.05, a = 0.05, p2 = 0.15, and b = 0.10.
Which confidence interval would lead you to Fail to Reject Ho? Test value: 10 Confidence Interval: 13.1 - 15.1 Test value: 10 Confidence Interval: 9.2 - 9.8 Test value: 5 Confidence Interval: 5.6 - 6.9 Test value: 5 Confidence Interval: 4.5 - 6.3
7. Suppose annual snowfall in Big Bear City is normally distributed with mean average of 58 inches ($\mu$ = 58) and standard deviation of 10 inches ($\sigma$ = 10). What's the probability that a randomly selected year has more than 70 inches of snowfall? P (x ≥ 70) (6 pts) -1E99 μ 1E99 8. Test…
I see restriction of range here. A. yes B. no NEO Ezscore 300 S. Oishi et al./Journal of Research in Personality 58 (2015) 55-68 20000 25000 Elevation Difference r=-.40, p<.01 Fig. 1. The inversion between elevation difference (Highest Point Lowest Point) and extraversion in Study 3. Chapter 8…
1. Calculate the mean, median and standard deviation of the following data .29 .104 .207 .145 .105 .124 All work should be done by hand, cannot use any software, only use calculator
A student from the economics department conducted a study to identify the percentage of family income allocated to the purchase of groceries. She surveyed a random sample of 60 families and compiled the following numeric frequency distribution: Percentage family income Number of families 10-20%…
Problem 1: A random variable X whose probability density function is given by $$f_x(x) = 0.38\delta(x-2) + k \text{tri} \left(\frac{x-2}{3}\right).$$ Another random variable Y is related to X through Y = 2X-3. Find 1. The value of k 2. The expected value and the variance of X 3. The probability…
Let the joint MGF of (X,Y) be: $$M(s,t) = e^{10s + 6t + 32s^2 + 2t^2 + 8st}$$ Then the distribution of X|Y = 7 is:
patients who had little or no evidence of retinopathy at baseline. Retinopa-thies are abnormalities of the retina that sometimes occur among diabetic patients and can result in substantial losses of vision in advanced stages. Patients were randomized to either Sorbinil, an aldose-reductase…
The random variable X is distributed exponentially with mean 1. Find the pdf of Y = (X – 1)².
Question 7 (1 point) Listen Which of the following are criteria for the One-Way ANOVA test? the samples must be independent the populations must be normally distributed the populations must have the same variance n≥ 30 for each sample np(1-p) ≥ 10 for each sample
If X = 131, σ = 26, and n = 33, construct a 95% confidence interval estimate of the population mean, μ. με (Round to two decimal places as needed.)
21. In the following regression, write the auxiliary regression used in the White test for heteroskedasticity: $$y_t = \beta_0 + \beta_1 x_{1t} + \beta_2 x_{2t} + u_t$$ 22. What is the null and alternative hypothesis of the White test of heteroskedas- ticity? 23. If the p-value of the F-test in…
Problem 4.1: (20 points): Statistics Suppose that the data given below were measured in an experiment. 15, 16, 5, 7, 20, 19, 8, 13, 6, 17, 6, 9, 19, 6, 14, 8, 20, 5, 18, 8, 13, 7, 18 a) (6 pts.) Construct a frequency table if the class width is 3. b) (6 pts.) Use the frequency table to draw a…
Use the t-distribution to find a confidence interval for a difference in means µ₁ – μ₂ given the relevant sample results. Give the best estimate for μ₁ - µ₂, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately…
4.195 Traffic Fatalities. According to Accident Facts, published by the National Safety Council, a probability distribution of age group for drivers at fault in fatal crashes is as follows. Age (yr) Probability 16-24 0.255 25-34 0.238 35-64 0.393 65 & over 0.114 Of three fatal automobile…
Data was collected on the dear population in Oregon for the last ten years. Reference the graph below to determine the initial amount of deer counted in the population. N(t) 320- 300- 280- 260- 240- 220- 200- 180 (6, 180) 160 140 120 100 80 Deer Population 0 1 2 3 4 5 6 7 8 9 10 Years t
Let $X_1$, $X_2$, ..., $X_n$ be IID random variables, where $X_i$ ~ Uniform (0, 1). Define the sample mean as $M_n = \frac{X_1 + X_2 + ... + X_n}{n}$ Use Chebyshev's inequality to find an upper bound on $Pr[|M_n - \frac{1}{2}| \geq \frac{1}{100}] \leq \frac{C}{n}$ Give the value of C correct to…
Mr. Ratajski wants to analyze his student's performance in Algebra II Accelerated for his students for the first semester. The semester one grade for his class are listed below: 86 78 72 89 81 85 40 93 80 76 79 88 92 94 44 90 92 78 65 68 79 85 90 88 99 94 a) Organize the numbers above in order…
6. Given Z is the standard normal variable, find a) P(|Z| > 1.75), b) P(|Z| < 2.05).
Question 3 A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of…
Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .179 .032 .026 2.023 a. Predictors: (Constant), AGE Model Sum of Squares df Mean Square F Sig. 1 Regression 23.784 1 23.784 5.812 .0175 Residual 720.238 176 4.092 Total 744.022 177 a. Dependent Variable: INCOME b.…
23. The nicotine content in milligrams (mg) in cigarettes of a certain brand is normally distributed with mean $\mu$ and standard deviation $\sigma = 0.1$mg. The brand advertises that the mean nicotine content of its cigarettes is 1.5 mg, but measurements on a random sample of 100 cigarettes of…
3) Complete the diagram below to determine the percentage of each portion of the normal distribution. Use the Empirical Rule to help you determine each portion. IT -3σ -2σ -σ μ +σ +2σ +3σ 68% 95% 99.7% 4) In a random selection of 50 freshman, each student's height (in inches) is measured and…
12. An ice-cream store has 31 flavours of ice cream and three types of cones (waffle, sugar, and plain). a) Determine the number of possible single-scoop ice-cream cones. b) How many two-scoop ice-cream cones are possible if waffle-chocolate- strawberry is considered different…
As a promotional gimmick, OHaganBooks.com has been selling copies of Encyclopædia Galactica at an extremely low price that is changed each week at random in a nationally televised drawing. The following table gives the frequency with which each price will be chosen and summarizes the…
Exhibit 14-6 You are given the following information about x and y. X Independent Variable y Dependent Variable 4 12 6 3 2 7 4 6 Refer to Exhibit 14-6. The sample correlation coefficient equals a. -.1905 b. .4364 c. .1905 d. -.4364
Question 3 (1 point) The greatest number that can belong to the class Class boundaries Lower class limit Class width Upper class limit
Thirty-four percent of US residents have blood type A-positive. If a random sample of 5 US residents is chosen, find the probability that at most one if the sample has A- positive blood type. .068 .323 .200 .448 .677
60 20 40 60 80 20 0 680 20 40 60 20 0 60 80 60 440 20 0 20 40 60 80 100 0 20 40 60 80 100 C 0 20 40 60 80 100 0 20 40 60 60 D 0 20 40 60 80 100 Which scatterplot has a correlation coefficient of 0.99? Scatterplot A Scatterplot B Scatterplot C Scatterplot D
2.2 The following data sample were obtained from student class test for statistical module. The number of students were grouped in the range of their test mark as in the table below: Range of marks in % Number of students 0-10 6 10-20 8 20-30 16 30-40 9 40-50 15 50-60 33 60-70 19 70-80 6 80-90…
Exercise 03.25 Algo (Measures of Variability) Question 4 of 8 Hint(s) Check My Work Consider a sample with data values of 26, 25, 20, 15, 32, 33, 29, and 25. Compute the range, interquartile range, variance, and standard deviation. Round to 2 decimals, if necessary. Range 18 Interquartile…
26. ______ test is not an appropriate test to examine the group difference with a continuous DV. O ANOVA O Dependent-Sample t-Test O Chi-square O Independent-Sample t-Test
2) An m&m fan is munching on some m&m's surfing the web when they come upon a site. According to the site, 24% of m&m's are blue, 20% are orange, 16% are green, 14% are yellow, 13% are red, and 13% are brown. They want to check if this is false. They take a bag containing several m&ms and finds…
84.6% of the times to prepare an order vary from the regression line by less than 1 hour. 95% of the times to prepare an order can be predicted accurately based on the dollar amount of the order. 84.6% of the variation in the times to prepare an order is due to factors other than the dollar…
Internet Local Men 256 543 799 Women 212 108 320 468 651 1119 16. Use the given table (above) of shopping data by modality and gender to find the indicated probabilities. a. When making a single selection find P(Internet or Men) a) 0.800 b) 0.903 c) 0.811 d) 0.798 e) None of the above b. When…
21) The p-value is 1.2 Points the same as the z statistic. a sample statistic a distance a probability
The categories, or grouping of data, collected for a specific measure are known as ______. a. variables b. attributes c. criterion d. reasoning
Quest 1260, 1446, 1106, 1269, 1443, 1424, 1118, 1132, 1177, 1115, 1156, 1262, 1215, 1236, 1243, 1169, 1437, 1191, 1401, 1439, 1365 Price of Refrigerators (in Dollars) Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative…
Percentage family income Number of families 10-20% 6 20-30% 14 30-40% 16 40-50% 12 50-60% 4 60-70% 8 a. Compute and interpret the (approximate) mean percentage of family income allocated to grocery purchase. (10)
Suppose you work for a smoothie shop and you want to assess whether the average transaction value at your shop is different from the competing smoothie shop on the other block. To do so, you randomly sample 19 of your shop's transactions and record a sample average of $9.75 and sample…
Practice: The Mean and Variance of Binomial Distribution 2 puntos posibles (calificados) Recall that the pmf of a Binomial distribution Binom (n, p), with known n can be written as: $$f_0(y) = exp\left(\frac{y\theta - b(\theta)}{\phi} + c(y, \phi)\right).$$ Refer to the answer of b (0) and $ to…
Problem 4. (25%) Let X and Y be independent random variables with common probability density function, in other words $$f_X(x) = \begin{cases} \exp(-x) & \text{if } x > 0 \\ 0 & \text{elsewhere} \end{cases}$$ $$f_Y(y) = \begin{cases} \exp(-y) & \text{if } y > 0 \\ 0 &…
6 The specifications for a certain type of surveillance system state that the system will function for more than 12,000 hours with probability of at least .90. Fifty such systems were checked and eight were found to have failed before 12,000 hours. These sample results cast some doubt on the…
1. In 2023, Southwest Airlines had 76% On-Time Percentage (OTP) for flights. Suppose 4 flights are randomly selected from Southwest Airlines, find the probability of each: a) All four are On-time (x = 4). b) None of the four are On-time (x = 0). c) At least one is On-time (x > 1). 2. Fantasy 5…
Question 1 A study of soft drink and smoking habits was conducted. Of 12,580 people who said they consume soft drinks weekly, 2694 said they were smokers. Of 14,873 who said they almost never consume soft drinks, 2497 were smokers. To find the point estimate to construct a confidence interval…
Suppose that $X_1$, $X_2$, ..., $X_n$ and $Y_1$, $Y_2$, ..., $Y_n$ are independent random samples from populations with means $\mu_1$ and $\mu_2$ and variances $\sigma_1^2$ and $\sigma_2^2$, respectively. $$U_n = \frac{(\overline{X} - \overline{Y}) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2 +…
For a normal variable X ~ N(μ = 27.3, σ = 5.7), find the probability P(28.35 < X < 29.15): P(28.35 < X < 29.15) = (Round the answer to 4 decimal places) Question Help: Video 1 Video 2 Video 3 Written Example 1 ☑ Message instructor Check Answer Jump to Answer Question 2 0/1 pt3 Details For a…
Group Statistics Fertilizer N Mean Std. Deviation Std. Error Mean Growth One 12 14.25 Two 12 13.08 4.181 4.660 1.207 1.345 Growth Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances Independent Samples…
MAT 102 703- Liberal Arts Math Test: Final Exam Question 7 of 12 The accompanying table gives the number of copies sold for 30 top-selling novels. Use data given in the table to construct a frequency distribution with a first class (in millions) of 50-99. samantha sanchez 05/14/24 7:42 PM This…
The diameters of metallic spherical engine components is a continuous random variable and is uniformly distributed between $$1.4 < X < 2.6$$ a) Determine the cumulative distribution function of the diameter. [5 points] b) Determine the proportion of diameters that exceed 2.1 millimeters. [6…
Consider the following exponential probability density function. $$f(x) = \frac{1}{2}e^{-x/2}$$ for $x \ge 0$ If needed, round your answer to four decimal digits. (a) Choose the correct formula for $P(x \le x_0)$. (i) $P(x \le x_0) = 1 + e^{x_0/2}$ (ii) $P(x \le x_0) = 1 - e^{x_0/2}$ (iii) $P(x…
Linear Combination of RVs Ex: Let Y = X₁ - X2 and assume a joint density function of two RVs X1 and X2 is given by $$f(x_1, x_2) = \begin{cases} 3x_1 & 0 \le x_2 \le x_1 \le 1 \\ 0 & \text{elsewhere} \end{cases}$$ Find the mean and variance of Y.
1. The joint pmf of two random variables X and Y is given by $$P_{X,Y}(x,y) = \begin{cases} c(x+y) & x = 1,2; y = 1,2,3 \\ 0 & \text{elsewhere} \end{cases}$$ (a) Find the constant c. (b) Find the marginal pmf of X and of Y. (c) Find the probability P[Y > X].
Question 4: The mean lifdetime of a sample of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation Of 120 hours. a) Test the hypothesis that the mean lifetime is at most 1600 hours. (probability of type I error =0.05). b) How large a sample of…
Problem 1 (25%) due 05-16-2024 A wire manufacturing company has inspectors to examine the wire for fractures as it comes out of a machine. The number of fractures is distributed in accordance with a Poisson process, having one fracture on the average for every 50 meters of wire. One day an…
7) Parameters are 1.2 Points numerical characteristics of a sample. numerical characteristics of a population the averages taken from a sample. numerical characteristics of either a sample or a population.
Which of the following statements is TRUE regarding older adults and fluid intake. Older adults require the same amount of fluids as younger adults. Older adults typically drink the recommended amounts of fluids. Older adults require less fluids than younger adults. Older adults require more…
5). Assume X, Y are independent random variables. X satisfies normal distribution with mean 0 and variance 4; Y satisfies normal distribution with mean 5 and variance 9. i. What is the distribution of X²? ii. What is the distribution of 3X? iii. What is the distribution of -4Y? iv. What is the…
4. a) Three parts are assembled in series so that their critical dimensions $x_1$, $x_2$ and $x_3$ add. The dimensions of each part are normally distributed with the following parameters: $\mu_1$ = 55, $\sigma_1$ = 2, $\mu_2$ = 65, $\sigma_2$ = 3 and $\mu_3$ = 92, $\sigma_3$ = 3. If the…
The lengths of pregnancies in a small rural village are normally distributed with a mean of 269 days and a standard deviation of 12 days. 15.[2] In what range would you expect to find the middle 50% of most pregnancies? Round your answer to the nearest tenth of a day. 16.[3] If you were to draw…
If the universal set U={0,1,2,3,4,5,6,7,9,11) has two subsets A={1,3,5,11} and B={0,2,3,9,11). Find: BUA A Question 6 (3 points) Listen Find the probability of the given event occurring: Receiving either a first or a second prize in a drawing involving 3 other people. In the first text box,…
What is the value of ?(X - 4)^2 for the following scores? Scores: 4, 1, 6, 5 62 74 14 0
Contingency Table Type of Heating By Delinquent in Payment? Count Yes No Totals Electricity 20 130 150 Heating Oil 15 20 35 Natural Gas 50 240 290 Propane 12 39 51 Totals 97 429 526 Use the JMP output below to report the correct p-value degrees of freedom and the ? Report the numbers as listed…
1) Lastik materyallerin testi için yapılan bir deneyde lastik yapımında kullanılan A katkı maddesi oranı ve materyal kalınlığı etken olarak alınmıştır. Araştırmada bağımlı değişken 10 kilogramlık bir ağırlığı yerden bir metre yukarı kaldırmak için geçen süre olarak belirleniyor. Katkı maddesi…
The lives of all televisions manufactured by the Lucky Goldstar ("LG") company has a normal distribution with a mean of 60 months and a standard deviation of 12 months. LG provides a replacement warranty - all television found to be defective in the first two years, the company will replace…
1. Four catalysts that may affect the concentration of one component in a three- component liquid mixture are being investigated. The following concentrations are obtained from a completely randomized experiment: Catalyst Observations…
20) Compute the probability of X successes. n = 4, X = 3, p = 0.1 ID: BESB8e 5.3.4-1
Suppose you work for a smoothie shop-and you want to assess whether the average transaction value at your shop is different from the competing smoothie shop on the other block. To do so, you randomly sample 19 of your shop's transactions and record a sample average of $9.75 and sample standard…
11. In a randomized control trial for Calorie-Reduction (CR), 27 participants had a sample mean weight loss of x = 5.42 kg and standard deviation of s = 9.39 kg. What is the 95% confidence interval (CI) and margin of error (ME) for the population weight loss, u, of all participants on…
01. (2p) 50 Samples of a part of 3D-printer are classified as shown in the table below on the basis of conformity to Depth and Width specifications The number of parts which conform to Depth Specifications Yes No The number of parts which conform to Width…
At least 12% of car crashes occur within 2 miles of the motorists home. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage). $H_0: p$ $H_1: p$ Use the following codes to enter the following symbols: $\geq$ enter $\ge$ $\leq$ enter $\le$ $\neq$…
Let Y denote a random variable that has a Poisson distribution with mean λ = 3. (Round your answers to three decimal places.) (a) Find P(Y = 5). (b) Find P(Y ≥ 5). (c) Find P(Y < 5).
1) Mr. Ratajski wants to analyze his student's performance in Algebra II Accelerated for his students for the first semester. The semester one grade for his class are listed below: 80 78 72 89 81 85 40 93 80 75 79 88 92 94 44 90 82 78 65 68 79 85 90 88 99 94 a) Organize the numbers above in…
[ ] 17. [10=2+8 pts] According to the American Red Cross, 7% of people in the United States have blood type O-negative. A simple random sample of 300 Americans is selected and it is determined whether each person in the sample has O-negative blood type. a) Verify the condition that allows us to…
In hypothesis testing, in order to reject the null, our P value (P) must be ______ our preset Alpha (a) Value. O greater than less than O equal to O in opposition to
Imports and Exports A random sample of countries shows the value of U.S. exports and the U.S. imports for each country for a recent year. The data are in hundreds of millions of dollars. Assume the independent variable is…
In a standard Normal distribution, if the area to the left of a z-score is about 0.5712, what is the approximate z-score? Click here to view page 1 of the Standard Normal Table. Click here to view page 2 of the Standard Normal Table. z= (Round to two decimal places as needed.) Area under the…
There is no independent valid test for ADHD. True False There is no independent valid test for ADHD. True False
NAME: SCORE: Decimal Averages Independent Practice INSTRUCTIONS: Find the averages for each set of data. Round answers to the nearest hundredth 1. 10.2, 2.17, 5.67, 11.70, 0.72 2. 97.87, 78.25, 7.80, 34.27, 40.42 3. 10.51, 1.44, 39.32, 64.09, 27.38, 50.66, 76.37 4. 65.81, 26.96, 64.24, 1.79,…
1(b) The graph below has several tables representing the probability distribution (CO1) values of the given 5 variables. $e^0$ 0.7 $e^1$ 0.3 Exam level IQ level $i^0$ 0.8 $i^1$ 0.2 $i^0$, $e^0$ $m^0$ 0.6 $m^1$ 0.4 Marks Apti. score $i^0$, $e^1$ 0.9 0.1 $i^1$, $e^0$ 0.5 0.5 $i^1$,…
4. Randi commutes to work in a very high traffic area. There is a 95% chance that she hits a red or amber light during her morning drive. What is the expected number of drives before Randi has a drive with no red or amber lights? (3 marks)
1. A Social Science student conducted a study to assess the association between two variables measured at a categorical level for Creativity and Online gaming activities among adolescents. The following data were obtained. Online gaming activities Low Moderate High Above average…
2 Problem set for Section 5.2 Expectation 1. Let X have the discrete uniform distribution on 7 letters (meaning, it models rolling a balanced 7-sided die). 1 (a) Calculate the mean μ (b) Calculate the standard deviation σ 2. When you give a casino $5 for a bet on the "pass line" in a casino…
Question 2: In another part of the paper, they look at the characteristics of people who were classified as 'low' or 'moderate' chocolate consumers. Total daily chocolate consumption Low (<= 10 g/day) Moderate (> 10g/day) Total Men 19 34 53 Women 29 49 78 Total 48 83 131 a) What would be an…
D Question 20 1 pts A factor is considered a confounder if that factor is a known risk factor for a disease of interest and if that factor is associated with an exposure of interest. (mark True or False)
A large school district receives funding to assess the effectiveness of a new reading curriculum. They have enough money to test the curriculum with a large sample of students within the district. Briefly explain which type of participant sampling (probability or non-probability) is more ideal…
3. (15 pts.) Un fabricante de equipo deportivo desarrolló un nuevo sedal para pesca sintético que, según afirma, tiene una resistencia media a la rotura de 8 kilogramos con una desviación estándar de 0.5 kilogramos. Pruebe la hipótesis de que µ = 8 kilogramos contra la alternativa de que µ ≠ 8…
Find the value of the linear correlation coefficient r. x 57 53 59 61 53 56 60 y 156 164 163 177 159 175 151 (1 point) Ο 0.109 -0.054 Ο 0.214 Ο -0.078
b) The number of roses and the number of lily flowers are noted every week at a garden during an observation. The observation readings of 4 successive weeks are as follows: Compute the coefficient of determination and interpret the result. (7 marks) Rose Lily 2 4 3 1 6 2 5 3 $$r = \frac{n(\sum…
7. (13 points) CSUN Statistics department purchased 24 Dell laptops from a dealer in order to have a supply on hand for tests for use by students who forget to bring their own. Although the department was not aware of this, five of the laptops were defective. When a test is being written,…
2. A linear probability model (LPM) has been estimated using Ordinary Least Squares (OLS) with a sample of N = 500 observations, yielding the following results: Y = 12.4 + 3.4X1,i – 0.2X2,i + ûi (23) (3.2) (-0.9) Knowing that the values in parentheses correspond to the individual significance…
2. The random variable X has the following probability density function: $$f(x) = \frac{2}{\lambda^2}xe^{-x^2/\lambda^2}, x \ge 0$$ where $\lambda$ is a positive parameter. (15 points) (a) It can be shown that $$E(X) = \frac{\sqrt{\pi \lambda}}{2}$$ and $$E(X^2) = \lambda^2$$ Set up (but do not…
Determine the level of measurement of the variable. Ages of children: 5 years, 6 years, 7 years, 8 years, and 9 years Choose the correct answer below. Ratio Nominal Interval Ordinal
Problem 4.4 (20 points): Continuous RV The cumulative distribution function of random variable X is $$F_x(x) = \begin{cases} 0, & x<-1 \\ \frac{(x+1)}{2}, & -1\leq x<1 \\ 1, & x\geq 1 \end{cases}$$ a) What is the probability P[X > 1/2]? b) What is the probability that P[-1/2 ≤ X <3/4]? c) What…
State Prison Dollars Violent Crime per Capita (x) Rate (y) Iowa 150 6.57 Idaho 51 2.23 Maine 199 4.20 Nebraska 55 2.81 Tennessee 179 6.91 N=5
9. In 2023, FICO scores a mean of 715 (μ = 715) and a standard deviation of 42 (σ = 42). a) Find P95, the 95th percentile, the score that separates the bottom 95% from the top 5%. 0% 50% 100% b) Find P99, the 99th percentile, the score that separates the bottom 99% from the top…
Question 42 0.2 pts Lung cancer is the leading cause of cancer-related deaths in the United States. Researchers are interested in studying the relationship between aspirin use and lung cancer - for example, whether the use of aspirin reduces the risk of lung cancer. To study this, they…
Participants in a study investigating the relationship between coffee consumption and exercise were asked to report the number of steps per day they completed over the past week. The table below gives summary statistics for the daily step count of study participants based on the amount of…
Pregnant Woman Before Treatment After Treatment Difference Sign 1 8 3 2 10 7 3 6 5 4 8 10 5 11 10 6 8 2
Suppose the X is a continuous random variable whose probability density function is given by $$ f(x) = \begin{cases} kx, & 0 \le x < 3, \\ 2 - \frac{x}{2}, & 3 \le x \le 4, \\ 0, & \text{otherwise} \end{cases} $$ (a) What is the value of k? (b) What is the cumulative distribution function of X,…
$f(y) = (\theta + 1)y^\theta$, $0 < y < 1$, $\theta > -1$. (a) Derive the maximum likelihood estimator of $\theta$. Show all working.
An instructor wants to use two exams in her classes next year. This year, she gives both exams to the students. She wants to know if the exams are equally difficult and wants to check this by looking at the differences between scores. If the mean difference between scores for students is "close…
In a normal distribution, what z- score cuts off the top 15% of the distribution? z = -0.91 z = -1.04 z = +0.91 z = +1.04
4. (15 pts) Consider a coin. Assume that, when we toss it once, the probabilities on the outcomes H, T are given by P({H}) = p and P({T}) = q, where p, q > 0 and p + q = 1. Now, we toss the coin three times and asume that one or two tossings does not affect the rest. Consider the following…
MLE for Poisson distribution Calculate likelihood function $$L(\lambda) = \prod_{i=1}^m P(x_i | \lambda)$$ $$L(\lambda) = \prod_{i=1}^m \frac{e^{-\lambda} \lambda^{x_i}}{x_i!}$$
19. An instructor gives a test before and after a tutoring session and results from randomly selected students are given here. Test the claim that the tutoring improved scores. Before 64 51 67 87 51 67 34 71 81 After 70 56 64 89 51 77 42 71 90 a. Find the P-value b. Will the null hypothesis be…
A marketing team needs to complete a marketing campaign project which involves six activities. The network diagram for the project is presented below. A B Start End C D E F The team has the following partially completed estimates of means and standard deviations. Some are at the activity level,…
Let x be the number of successes observed in a sample of n = 6 items selected from a population of N = 12. Suppose that of the N = 12 items, M = 7 are considered "successes." Find the probability. (Round your answer to four decimal places.) the probability of observing at most two successes You…
Find the sample size needed if a 98% confidence interval has a 'margin of error' of 4% if ... You feel safe using an estimate for p of .13 You are going to play it as safe as possible and use p of .50 Find the sample size needed if a 99.8% confidence interval has a 'margin of error' of 0.5%…
Problem 3 (25%) The joint probability mass function p(x, y) of the random variables X and Y is given by the following table. Find the conditional probably $P_{X|Y}(x|y)$ for all possible pair of (x,y). You can list all the probability as a table with format similar to the following…
Which of the following correctly describes the formula for the p-value in the mammography study, given an observation of $Y = 39$ deaths due to breast cancer in the treatment group of 31000? $P_{H_0}(T \le 39)$, the probability under $H_0$ to obtain the observed value or a more extreme value of…
6. $X_1, X_2, ..., X_n$ are a random sample from $N(\mu, 1)$. (a) Find the Cramér-Rao lower bound of the variance of unbiased estimators of $\mu$. (b) Show that the sample mean is the MVUE using (a).
Duration of the test: 60 mins. Only pocket calculator and the Formulas down any particular results. Signature 1. Suppose that we have a sample space with five equally likely elementary outcomes: E1; E2; E3; E4; Es Let A= { E1; E2} B={ E4;E5) a) Find P(A), P(B), P(C) b) Find P (AOC). c) Find…
Control group Exposure group 3 9 6 6 3 4 4 5 3 4 1 3 2 4 5 4 7 6 8 7 8 a. Test for hypothesis at a significant level of 0.05 if there is a difference between the two groups with regard to statistics anxiety levels. Show all your calculations and hypothesis-testing steps. (16 marks). b.…
A statistics professor randomly selects 20 of her students and records their final exam scores. 89 15 67 84 14 78 59 45 85 67 96 15 23 46 19 84 17 39 24 83 Find the percentile for 24. Find $P_{83}$ (the value that corresponds to the 83rd percentile). 65 84 Done
You wish to test the following claim ($H_a$) at a significance level of $\alpha = 0.01$. $H_o: \mu = 57.1$ $H_a: \mu \neq 57.1$ You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size $n = 16$ with mean $M = 44.5$ and a…
e. What is your decision regarding $H_o$? What is your decision regarding $H_o$? Do not reject There is insufficient evidence to conclude that the population mean is greater than 20.
Kuhn and Pease (2006) compared hypothesis-testing skills of 11- to 12-year-olds with those of young adults. They were asked to choose accessories for a charity giveaway, then were given data based on their selections. To use the data most effectively, participants needed to attend to their…
Example If {Yt} is from the following model Yt = 0.5 Yt-1 + 0.2 Yt-2 + Et - Et-1 Et ~WN(0.1). (1) Express Yt = FYt-1 + Vt. Vt = [Ut] 0 Ut = Et - Et-1 (2) Is {Yt} stationary (check the eigenvalues of F) (3) Express Yt = Et + Y1 Et-1 + Y2 Et-2 + ... Give Y1 value. (4) Write the relations…
Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that less than 15% of firms in the manufacturing sector provide child-care benefits to their workers. A random sample of 350 manufacturing firms is selected and asked if they offer…
2. What is power of a test? Select all that applies. ✔1-P(type II error) PHA (reject Ho) 1-P(type I error) PHo (reject Ho) x
A salesman has 8 presentations scheduled for the coming month. Historically, 30% of her presentations have resulted in sales. It is reasonable to assume that her chance of making a sale in any given presentation is not affected by what happens in any other presentation. Find the following…
At a recent company picnic with over 2000 guests, an outbreak of food poisoning occurred. A doctor suspects that the potato salad may be related to the food poisoning. A random sample of 200 guests asked about their symptoms and whether or not they ate the potato salad. The data is presented in…
Let z be a standard normal random variable with mean ? = 0 and standard deviation ? = 1. Find the value c that satisfies the inequality. (Round your answer to two decimal places.) P(z > c) = 0.0233 c = You may need to use the appropriate appendix table to answer this question.
a-1. Construct a contingency table that cross-classifies the data by Age and Brand. Provide the frequencies in the accompanying table. Brand Age A B C ≥ 35 years old (0) < 35 years old (1) a-2. How many of the purchases were for Brand A? Number of purchases for Brand A a-3. How many of the…
Four hundred draws are made at random with replacement from a box. The average of the draws is 28.5 and the SD is 20. Someone claims that the average of the box equals 26.5. Is this plausible? Find P and decide whether the average of the box equals 26.5 or is more than 26.5. Selected Answer: P…
1 Please round Pi to three decimal places. 3 2 Find the absolute value of -22. Important Functions 3 Generate a random number between 0 and 1 and display it in percentage (for example, 99.99%). 5 4 Generate a random number between 1 and 100. 65 What is 15 squared? 7 6 What is 8 cubed? 8 7 What…
2. Suppose you are modeling the number of accidents occurring at a particular intersection each month. Which distribution would you use for this scenario? Justify your choice. (5 pts)
Answer the question for a normal random variable x with mean μ and standard deviation σ specified below. (Round your answer to four decimal places.) μ = 1.3 and σ = 0.18. Find P(1.00 < x < 1.10). USE SALT P(1.00 < x < 1.10) = You may need to use the appropriate appendix table to answer this…
Scenario 1 (Part A): Dr. Ramirez investigated the association between college students' anxiety symptoms and help seeking behaviors. She used a subset of items from the Anxiety Symptoms Questionnaire (ASQ) to assess the frequency of anxiety symptoms. She used a new survey she created to assess…
3. A certain characteristic is said to be related with the eye colour. A sample of 160 randomly selected individuals are obtained and the results are tabled below: Has characteristic? Yes No Eye colours Brown Blue Others 20 35 15 35 25 30 Let R denotes the event that a selected individual has…
Question 1 Which source of bias is most relevant to the following situation: The CEO of a company asks employees to call an anonymous phone-line to report concerns about their work environment. self-interest study voluntary response bias nonresponse bias or missing data perceived lack of…
Before revealing your final exam grades, your instructor tells you that there is a linear relationship and a correlation of 0.7 between the exam 2 grades and the final exam grades. The average grade on exam 2 was 86 and the average grade on the final was 91. The standard deviation on exam 2 was…
1. In the linear probability model (LPM): a. The model parameters can be estimated consistently and efficiently using the method of Ordinary Least Squares (OLS) estimation. b. The dependent variable can't take discrete values, Y = 0 and Y = 1. c. The error term of the model is…
A researcher was interested the relationship between fetal heart beat rate at 7 weeks gestation and healthy Apgar scores 5-minutes after full-term birth (a measure of how well the infant is doing after birth). Healthy fetal heart rates at 7 weeks range from 110-160 bpm. Apgar ratings of 7 or…
Find the normalizing constant of the pdf satisfying $$f(x) \propto xe^{-x^2} 1(x>0).$$
Caffeine in Tea Bags In a recent study, researchers found that the average amount of caffeine in tea bags is 26 mg. The standard deviation of the population is 3 mg. If a random sample of 45 newly manufactured tea bags has a mean of 24.8 mg of caffeine, can it be concluded that the new brand of…
17. Describe how the mean compares to the median when a distribution is skewed to the right. OA. Mean > median OB. Mean < median C. Mean = median OD. Both mean and median = 0
A builder claims that heat pumps are installed in more than 70% of all homes being constructed today in a city. Test this claim at the 10% significance level if a survey showed that 11 out of 15 homes had heat pumps installed. (A) State the null and alternate hypotheses. (2 points) (B) What is…
6 The random variable X is distributed normally with a mean of 300 and a standard deviation of 5. Find the following: a P(X > 305) b P(X < 291) (AC 4.2) C P(X < 312) d P(X > 286)
Use the following data set and conduct a two-talled test of significance using the Pearson r. Use alpha = .05. Label your answers. A. What are your null and alternative statistical hypotheses for this correlation? B. What are your degrees of freedom AND what is the critical value? C. Calculate…
Provide an appropriate response. Find the equation of the regression line for the given data. Round values to the nearest thousandth. -5-341-1-20 X y -10-89 v=2.097x-0.552 023-4 1-2-6-13 6-8 = 0.522x - 2.097 =-0.552x + 2.097 y = 2.097x + 0.552 0000
El siguiente ejercicio es ficticio. Un veterinario le inyectó 10 mg del antibiótico gentamicina (por cada kilogramo de peso corporal) a cinco ovejas hembra sanas de tres años. Las concentraciones de gentamicina en la sangre de estas ovejas, luego de una hora y media (en µg/ml), fueron las…
Evaluate the expression.\ $frac{sqrt{15}}{sqrt{8}}$\ $frac{sqrt{15}}{sqrt{8}} approx oxed{}$ \ (Do not round until the final answer. Then round to two decimal places as needed.)
Question 7 1 pts What is the mode on the graph below? 12 10 8 6 4 2 0 1 2 3 4 5 6 7 7 Two modes: 11 & 9 Two modes: 6 & 7 No mode
1. Prove the following properties of covariance: • cov(X, Y) = cov(Y, X) • cov(X,X) = Var(X) (15 pts) • cov(aX, Y) = a cov(X, Y) for any constant a • cov(X+c, Y+d) = cov(X,Y) where c and d are constants
Let X(t) be a continuous-time random process defined by X(t) = Acos(ωt+Φ) where the random variables A ~ Uniform (0,1) and Φ ~ Uniform (0,2π) are independent. The autocovariance function of the process X(t), Cx(t, t_0), is given by 0 1/6 cos(ω(t_1 - t_0)) 0 1/4 cos(ω(t_1 - t_0)) 0 1/3 cos(ω(t_1…
4.5.11. Let $Y_1 < Y_2 < Y_3$ be the order statistics of a random sample of size $n = 3$ from a distribution with pdf $f(x; \theta) = 1/\theta$, $0 < x < \theta$, zero elsewhere, where $0 < \theta$. The hypothesis $H_0: \theta = 1$ is rejected and $H_1: \theta > 1$ is accepted if the observed…
We perform a two-tailed hypothesis test on the population correlation coefficient between movie goers' snack spending and their age, at a = 0.05. For this, we collect a sample of 25 moviegoer's age and snack spending and the sample correlation coefficient r = -0.373. a. [2pts] Specify both the…
1. A Social Science student conducted a study to assess the association between two variables measured at a categorical level for Creativity and Online gaming activities among adolescents. The following data were obtained. Online gaming activities Low Moderate High Above Creativity average…
Estimated Mean 1.525 Hypothesized Mean 1 T Ratio 2.11662 P Value 0.02036 Two sided Low Side High Side Sample Size = 40 In the example above, how many p-values would we be able to reject the null hypothesis for? NOTE - When doing statistical tests, we only choose one alternative hypothesis to…
This study is based on Live-Long, a health shop specializing in natural foods and products. (i) 45% of customers visiting the shop spend more than R 500 on purchases. Consider a random sample of eight customers visiting the shop. (a) Write down four conditions that must be satisfied in order to…
(2pt) Consider a population of size N and simple random sampling (without replacement) with sample size n. Assume that the population takes values {$x_1$, ..., $x_N$} where $x_i$ ∈ {0,1} and that the proportion of 1's satisfies $\frac{1}{N}\sum_{i=1}^N x_i \to p$ as $N \to \infty$ and $p \in…
Question 10, 2.2.22 Part 2 of 8 The data to the right represent the number of customers waiting for a table at 6:00 P.M. for 40 consecutive Saturdays at Bobak's Restaurant. Complete parts (a) through (h) below. OC. The data are continuous because there are a finite or countable number of…
Before experimental drugs can be brought to market, they must undergo many rigorous trials to ensure they deliver their medical benefits effectively and safely. One method that is commonly used in this process is to compare the effects of a drug to that of a neutral placebo in double-blind…
Of the two given p-values, which provides more evidence against Ho? p-value = 0.002 p-value = 0.37
QUESTION 6 In the regression model Y₁ = ẞ0 + B1Xj+B2Di + B3(Xjx Dj) + uj, where X is a continuous variable and D is a binary variable, to test that the two regressions are identical, you must use the: OF-statistic for the joint hypothesis that ẞ2 = 0, β3=0. Ot-statistic separately for ẞ3 =…
In a survey, 1000 adults were asked to identify "what is inappropriate in the workplace." Of the 1000 subjects, 53% said that jeans were not appropriate in the workplace. a. What is 53% of 1000? b. Among the 1000 respondents, 730 said that hats are unacceptable in the workplace. What percentage…
Q9. (a) Let X = (X1 X2 X3)' ~ N3(µ, I) with µ = (2 – 3 1)'. Then obtain the distribution of (i) 3X1 - 2X2 + 5X3 and (ii) (X1-X2 X2-X3). 10
Two of the three conditions for a t-test between means are The samples must be randomly pooled The samples must be randomly selected The samples must be dependent (paired) The samples must be independent
For a population data set, $\sigma = 17.20$. a. What should the sample size be for a 98% confidence interval for $\mu$ to have a margin of error of estimate equal to 6.80? n = b. What should the sample size be for a 95% confidence interval for $\mu$ to have a margin of error of estimate equal…
Bob makes the forecast for the five months of sales. Compared with the actual values of sales for these six months, please compute the mean absolute error (MAE), mean squared error (MSE), and mean absolute percentage error (MAPE). Months January February March April May Actual…
A doctor would like to estimate the mean difference in height of pairs of identical twins. The doctor randomly selects 8 pairs of identical twins and determines the current height, in inches, of each twin. The data are displayed in the table. Pair Twin 1 Twin…
2.1 nomework practice How secure is your Job. A survey of Job Stability was taken below are results. responses very likely Frequency 351 Fairly Likely 403 Not too likely 1872 Not likely 4849 Total ? *please construct a relative frequency balance round answer two decimal places response Very…
1. Selecciona la respuesta correcta (3 ptos). A medida que el tamaño de una muestra de datos continuos aumenta (n→∞), el error estándar de la muestra: a. aumenta (SE → ∞) b. disminuye (SE → 0) c. no cambia Standard Error 2. Selecciona la respuesta correcta (3 ptos). A medida que el tamaño de…
4. Do the following: (a) Suppose that $X_1$, $X_2$ are discrete iid random variables with probability mass function $$p_{X_i}(x) = \begin{cases} 0.4 & x = 0 \\ 0.3 & x = 1 \\ 0.3 & x = 2 \end{cases}$$ i. (6 pts) Compute the joint probability mass function $p_{X_1,X_2}(x_1, x_2)$. ii. (6 pts)…
Suppose that Teddy graphs the temperature and the number of walks he's been hired to shovel. walks shoveled 16 • (-10,14) 14 (0,10) 12 10 (-5,11) (5,8) 8 6 4 (0,7) (20,6) 2 (32,3) -10 0 10 20 30 40 temperature + Calculate the what is the y-intercept (y'=a+bx) for the line of regression.…
56 Out of 500 people sampled, 145 have lied to a family member in the past month. Based on this, construct a 99% confidence interval for the true population proportion of people who have lied to a family member in the past month. Give your answers as decimals, to three places <p<
Problem 2. (25%) Let the joint probability density function of random variables X and Y be given By $f(x, y) = (\frac{2}{9})y * exp(-x)$ if x>0, 0<y<3 f(x,y)= 0 elsewhere Find the marginal probability density functions of X and Y.
In Ms. Tanti's geography class, • 60% of the students are Canadian • 28% of the students are of Chinese origin • 15% are Canadian and of Chinese origin. a) Construct a Venn diagram to represent this information Canadian Chinese b) What is the chance that a student drawn at random would be: i)…
Suppose you work for a smoothie shop and you want to assess whether the average transaction value at your shop is different from the competing smoothie shop on the other block. To do so, you randomly sample 19 of your shop's transactions and record a sample average of $9.75 and sample…
EXAMPLE 3.2 There are four batteries, and one is defective. Two are to be selected at random for use on a particular day. Find the probability that the second battery selected is not defective, given that the first was not defective.
Regression Equation in Uncoded Units Y= 64.375 +3.125 A-0.625 B + 6.875 C-4.375 AB-9.375 A°C+4.375 B°C + 6.62 Ct Pt Question: Use steepest Ascent method to optimize the response. Must show 4 steps for steepest ascent method (Ctpt means center point)
The vapour pressure of water increases with temperature as shown by the formula p = C * e ^ ( - ( ΔvapH^0 ) / ( R * T ) ). The data in the table below shows the vapour pressure of water (in mmHg) at varying absolute temperatures (in…
4. NBA All-Star James Harden has a career Free-Throw percentage (FT%) of 86% (p = .86). In a sample of 50 free-throws (n=50), use the binomial distribution to find each probability: a) Getting exactly 40 FTs (x = 40). (12 pts) b) Getting at most 40 FT (x ≤ 40). c) Getting at most 45 FTs (x ≤…
Compute the range for the set of data. 69, 147, 28, 101, 177 A. 149 B. 104.4 C. 177 D. 28
The null hypothesis of mean profit is 120 SR with population standard deviation = 10. In a sample of n=50 shops, the sample mean is 125 SR. Test the null hypothesis for the alternative hypothesis ≠ 120 SR (use a = 0.05). What is the p- value? nswer:
Twenty students completed statistics course. Each student took a midterm exam and a final exam. Summary statistics of the exam scores are given below. Exam Mean Standard Deviation Midterm 124 50 Final 129 56 In addition, the correlation coefficient equals 0.88. One of the students, Kelly,…
Question 1 [15] Consider the variables listed in 1 to 5 below, that are in a financial report of the Johannesburg stock exchange. Indicate for each of the random variables: (1) the type of the variables if it is a quantitative (numeric), categorical, discrete or continuous; and (2) the…
Complete the following relative frequency table. (Round to the nearest percent as needed.) Relative Relative Frequency Frequency Tar (mg) (Nonfiltered) (Filtered) 2-6 % % 7-11 % % 12-16 % % 17-21 % % 22-26 % % 27-31 % % 32-36 % % Frequency Distributions Tar (mg) in Nonfiltered Tar (mg)…
Considering the following constraints in a linear programming. 3x + y ≤ 50 2x + 3y ≤ 40 x ≤ 15 y ≤ 10 x ≥ 0 y = 0 Question 5 If the objective function is max 6x + 8y, what is the optimal solution for (x,y) with the above constraints? ( ). Rounding to 2-decimal points if needed. 4 pts
1) The Governor of a state has started a program to encourage people to exercise regularly. A concern of critics is that it appears to target women more than men. One year after the program began, a random sample of 800 men and 750 women were selected. Of the men selected, 384 exercise…
Exercise 3.1 - Decide whether or not each statement is necessarily true. 1. If A and B are mutually exclusive events and P(B) > 0, then P(A/B) = 0. 2. I have two dice. Die 1 is a normal die, that is, it has faces and each is obtained with probability. Die 2 is unusual: it has faces, and again…
Question 7 3 pts A researcher studying the proportion of 8 year old children who can ride a bike, found that 319 children can ride a bike out of her random sample of 885. What is the sample proportion? Round to 2 decimal points (e.g. 0.45).
HW Score: 6.25 Points: 0 of Question 2, 3.2.RA-12 Find the population standard deviation for the given data. 9, 16, 30, 35, 40 Select the correct choice below and fill in the answer box to complete your choice. (Round to two decimal places as needed.) A. The standard deviation is s = B. The…
2. The sample mean age of n=20 diabetic patients is 50 years and the sample variance is 100. Find the 99% confidence interval for the population mean age. Answer:
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