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Intro Stats / AP Statistics Q&A Archive of March 31, 2025

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March 31 of 2025

A population of plant heights has a mean of μ = 13 and standard deviation of σ = 2. What is the probability of an individual plant having a height between 10 and 16? a. 13.36% b. 68.27% c. 86.64% d. 93.32%
A research assistant determines they will need to randomly assign 20 participants to one of three groups. If they were to compute a one way between subjects ANOVA what would be the degrees of freedom within groups?
If X is χ^2(23), find the following: (a) P(14.85 < X < 32.01). (b) Constants a and b such that P(a < X < b) = .95 and P(X < a) = .025. (c) The mean and variance of X. (d) (χ^2)_.05(23) and (χ^2)_.95(23).
Refer to the probability density function given: fX(x) = e −(x−β) , x > β > 0 a) Find a method of moments estimator (MoM) for β [1 mark] b) Find a maximum likelihood estimator (MLE) for β [1 mark]
Develop a three-week moving average for this time series. Compute MSE and a forecast for week 8.If required, round your answers to two decimal places. Do not round intermediate calculation.
According to Harper's Index, 40% of all federal inmates are serving time for drug dealing. A random sample of 20 federal inmates is selected. What is the probability that 5 or fewer are serving time
A fair six-sided die is rolled 180 times. What is the probability that the “3” is rolled exactly 35 times? find the approximate probability using the normal distribution without continuity correction
What is the SS, sample variance, and standard deviation of class B? Class A Time Class B Time 1 39 1 48 2 42 2 36 3 49 3 40 4 56 4 41 5 69 5 45 6 61 6 37 7 37 7 39 8 31 8 30 9 45 9 49 10 53 10 36
Circle of radius r has area A = πr2. If a random circle has a radius that is uniformly dis- tributed on the interval (0, 1), what are the mean and variance of the area of the circle?
Based on past results, there is a 0.008 probability of finding bacteria in the swimming piil area. Find the probability that a combined sample from two public swimming areas will reveal the presence of bacteria
If Z is a standard normal random variable (that is, has mean zero and standard deviation 1), what is the probability that Z is between -2 and 2, that is, what is P( -2 < Z < 2), rounded to 3 decimal places.
During the season, Charlotte's team scored the following total points for 6 games: 92 points, 95 points, 95 points, 101 points, 112 points, and 143 points. Calculate the range for the points Charlotte's team scored.
If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of two successes in 15 trials, the correct probability function to use is the _____.
Suppose the correlation between height and weight for adults is +0.80. What proportion of the variability in weight can be explained by the relationship with height? Question 20 options: A. 20% B. 36% C. 64% D. 80%
If 15% of adults in a certain country work from home, what is the probability that fewer than 60 out of a random sample of 500 adults will work from home? (Round your answer to 4 decimal places) Incorrect
In a large general education class, 40% (0.4) are science majors, and 60% (0.6) are liberal arts majors. Ten percent (0.1) of the science majors are seniors, while 50% (0.5) of the liberal arts majors are seniors.
Jonas gets a 92% on Exam 1, a 65% on Exam 2, a 89% on Exam 3, and a 95% on Exam 4. What is his average exam score (assuming all exams are weighted equally)? His average score is: _______ % (do not round your answer
of a kịnd." B. SCOPE OF PSYCHOLOGY Psychology as a discipline or branch of knowledge has it's own scope of study. Basically it studies human experiences and behaviour. It primarily looks into the factors that
Four students are running for class president: Liz, Sam, Sue, and Tom. The probabilities of Sam, Sue, and Tom winning are 1⁄4 , 1⁄10 and 3⁄20 , respectively. What is the probability that Tom loses?
A student visits a population of five local restaurants (N = 5) and rates each as follows: 4, 3, 6, 4, and 8. Using the computational formula, what is the SS and σ2? a. 17; 3.4 b. 20; 4 c. 18; 3.6 d. 16; 3.2
The mean of women’s heights is 63.5 inches and the standard deviation is 2.5 inches. Select the two heights that define the lower and upper bounds of a range that encompasses about 99.7% of all women’s heights.
The probability that any one customer purchases a product warranty is 0.4. What is the probability that exactly 4 customers out of the next 10 will purchase a warranty? Answer to four decimal places.
Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy. (a)Mean absolute errorIf required, round your answer to one decimal place.
Consider a binomial experiment with n=20 and p=0.70. a. Compute f(12) (to 4 decimals). b. Compute f(16) (to 4 decimals). c. ComputeP(x>or equal to 16) (to 4 decimals). d. Compute P(x
suppose the time spent by a randomly selected student who uses a terminal connected to a local time sharing computer facility has a gamma distribution with mean 20 min and then variance 80 min, what are
The set of values of the statistic so obtained, one for each sample, constitutes what is called: Question 48 options: A. Sampling distribution B. Systematic sampling C. Stratified sampling D. Cluster sampling
onas gets a 92% on Exam 1, a 65% on Exam 2, a 89% on Exam 3, and a 95% on Exam 4. What is his average exam score (assuming all exams are weighted equally)? His average score is: _______ % (do not round your answer
Let X1, X2 be iid N(θ,1) (0 ≤ θ ≤ 1) and define the following decision rules: δ1 = 1 2 X1 + 1 2 X2; δ2 = 1 4 X1 + 3 4 X2; δ3 = 2 3 X1; and δ4 = 2 3 δ1. Consider squared error loss.
A certain drug causes liver damage in 50 % of patients. Suppose the drug is to be tested on 100 patients. How many patients would we expect to see with liver damage following use of the drug?    
It will be convenient to do a telephone survey in rural areas in China since, according to the Ministry of Information Industry reports, 40 percent of households have at least one fixed-line telephone. True False
suppose the first year salaries of uhcl graduates is normally distributed with a mean of 55000 also 7% uhcl graduates have first year salaries greater than $106000 what should be the standard deviation?
Box 1 contains 5 Red and 3 Black balls. Box 2 contains 3 Red and 1 Black ball. Box 3 contains 4 Red and 2 Black balls. If a Box is selected at random and a ball is drawn, find the probability it will be Red?
One study involving heavy use of phones showed the mean of the battery life to be 11.25 hours with a standard deviation of 2.2hours. Find the probability that with heavy use the life exceeds 12 hours
The alternative hypothesis is: the average amount of money spent at the PSU Bookstore is less than $100. We are using a significance level of 0.05. The Z statistic is 1.70. What’s the correct conclusion?
In a recent poll, 100 people were asked if they liked broccoli, and 69% said they did. Based on this, construct a 90% confidence interval for the true population proportion of people who like broccoli.
Find the moment-generating function for the gamma distribution with parameters a and e. HINT: In the integral representing E(e'*), change vari- ables by letting y = (1 - 0f)x/e, where 1 - 0t > 0.
The round off error when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5 mm. Round all answers to one decimal place, where your answer is not a whole number.
If Z is N(0,1) find (a) P(.47 < Z ≤ 2.13). (b) P(-.97 ≤ Z < 1.27). (c) P(Z > -1.56). (d) P(Z > 2.78). (e) P(|Z| < 1.96). (f) P(|Z| < 1). (g) P(|Z| < 2). (h) P(|Z| < 3).
For the given confidence level and values of x and n , find the following. =x44 , =n99 , confidence level 99.8% Find the standard error. Round the answers to at least four decimal places, if necessary.
to estimate the proportion of teen traffic deaths in Texas last year that was caused by speeding, determine the necessary sample size for the estimate to be accurate to within .05 with confidence .99
A local news agency is interested in studying unemployment rates across the state. The researchers will randomly select 1000 people from each state county and gather all relevant data from those selected.
GRADES 7What is the final conclusion? Select the BEST option for each blank.We[ Select ]the nullhypothesis because the P-value is less than or equal to the 5% significance level. We therefore[ Select ]that
In a classroom there are 105 students. 58 of them are male. There are 49 seniors in the class and 28 of the females are seniors. What is the probability that a randomly chosen student is a male and a senior
(d) On the basis of clinical trials, the probability of efficacy of a new drug is 0.760. A. Subjective method B. Classical method C. Empirical method D. It is impossible to determine which method is used.
Consider the following game. You pick a card from a deck and each time you select an ace, you get $260. For all other cards you must pay $13. What is the expected value of the game? $32 -$12 $0 $8
A professor analyzes two sets of student test scores. Class A has a mean of 75 and a standard deviation of 10, while Class B has a mean of 80 and a standard deviation of 20. Which statement is correct?
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 88 minutes and a maximum of 100 minutes. What is the probability that a flight is between 89 and 91 minutes?
A population consists of 8 items. The number of different simple random samples of size 3 (without replacement) that can be selected from this population is _____. Question 23 options: 24 56 512 128
a box contains 5 red and 7 blue balls. draw 6 balls with replacement. let u denote the variable equal to the number of red balls drawn. calculate the probability you get at most 3 red balls
A chi-square test for goodness of fit has df = 2. How many categories were used to classify the individuals in the sample? Group of answer choices 2 3 4 Cannot be determined without additional information
Given a standard normal distribution, find the value of k such that P(k < Z < −0.18) = 0.4197. Hint: Find area (pnorm) to the left of -0.18, subtract 0.4197 from it, find k (qnorm) of this difference.
It is construction season, and Google maps lists five different routes to your job. The travel times (in minutes) are: 21, 28, 14, 15, and 12. Calculate the population variance in route travel times.
A study finds a correlation coefficient of r = .52 and reports p < .05. The p is a _________. a. plausible significance approximation b. population value c. possibility assessment d. probability estimate
If the probability that an event will occur is three elevenths311, then the probability that the event will not occur is eight elevenths811, and the odds in favor of the event occurring are ________.
Find the probability that the sample mean is more than $75,000. Report your answer to 4 decimal places. If this is a probability that cannot be determined, then state unknown as your answer.
A sample of 240 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 15. Determine the 99% confidence interval for the population mean.
A population of birth weights has a mean of μ = 8.1 and a standard deviation of σ = 0.1. What is the probability of an individual weight being greater than 8.4? a. 99.87% b. 15.87% c. 2.28% d. 0.13%
a. Construct a 9999% confidence interval to estimate the actual proportion of students enrolled in college or a trade school within 1212 months of graduating from high school in 20172017.
9) A Rasmussen Reports survey of a random sample of 1,000 US adults found that 43% believe it will help the economy. Conduct an appropriate hypothesis test to help answer the research question
When pulling a single card out of a well-shuffled deck, which card demonstrates that the events {Face card} and {Spade} are not disjoint? King of Clubs Ace of Spades Queen of Spades The Ten of Hearts
Let X and Y be continuous random variables with the following joint density function: f(x, y) = 3 4 (2 − x − y) for 0 < x < 2, 0 < y < 2, x + y < 2 0 otherwise Compute E[X | Y < 1]
What is a typical eye blink rate for an infant about 2 to 3 months old? Group of answer choices mopre than 10 blinks per minute ~ 7 to 8 blinks per minute ~1 blink per minute ~2 to 3 blinks per minute
Interpreting a P-value. In each case, indicate whether the statement is a proper interpretation of what a p-value measures. The probability of make a Type 1 error, if the null hypothesis, H0 is true.
A simple random sample of 12 observations is derived from a normally distributed population with a population standard deviation of 4.2. Is the condition that X⎯⎯⎯X¯ is normally distributed satisfied?
From a population of 200 elements, the standard deviation is known to be 24. A sample of 64 elements is selected. It is determined that the sample mean is 57. The standard error of the mean is _____.
What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.) 98% confidence, n = 24 90% confidence, n = 24
What is the minimum sample size is required to estimate a population mean with 90% confidence when the desired marginal bear is D equals 1.25 the standard deviation and a pre-selected samples 8.5
The average score for games played in the nfl is 21.8 and the standard deviation is 9.1 points. 17 games are randomly selected. Find the 15th percentile for the mean score for this sample size.
The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 23 minutes, inclusive. What is the probability that a person waits fewer than 8 minutes?
If x follows a Poisson distribution with a standard deviation of 7, what is the expected value of X? A) 49 B) there is not enough information given to find the expected value of X C) 25 D) 81 E) 9
The basic objective of a sample is to draw ____________________ about the population from which such sample is drawn. Question 49 options: A. Conclusion B. Characteristics C. Inferences D. Parameters
If 15% of adults in a certain country work from home, what is the probability that fewer than 48 out of a random sample of 400 adults will work from home? (Round your answer to 4 decimal places)
If people adopted healthy lifestyle behaviors such as regular exercise and a moderate diet, about ________ of cases of type 2 diabetes could be prevented. Question 8Answer a. 90% b. 70% c. 80% d. 60%
Given a confidence level value C (in decimals), the significance level α for a population with mean μ can be determined using the formula: Group of answer choices α = 1/C α = μ/C α = 1 - C α = μ - C
Someone flips 15 biased coins once. The coins are weighted such that the probability of a head with any coin flip is .85 (P = .85). What is the probability of getting at least 14 heads
Determine the margin of error for a confidence interval to estimate the population proportion for the following confidence levels with a sample proportion equal to 0.340.34 and nequals=100100.
The mean score of a placement exam for entrance into a manta class is 80, with a standard deviation for 10. Use the empirical rule to find the percentage of scores that lie between 60 and 80.
If X is a random variable having a Binomial distribution with parameters n and 𝜃, show that U = '(! $(" is a biased estimator of 𝜃. Is U an asymptotically unbiased estimator of 𝜃? Justify
Whats the probability of picking two Queens from a deck of cards without replacement? Pick the correct formula. ((4)/(52))((3)/(51)) ((4)/(52))((4)/(51)) ((4)/(52))((3)/(52)) ((2)/(52))((3)/(51))
determine whether or not there is a significant relationship between number of full-time jobs added and the two independent variables (full time voluntary turnover and total worldwide revenue)
How large a sample should be taken if the desired margin of error is $400? Use a rounded z value (2 decimals) in your calculations .Round your answer for n to next whole number. $170?
Suppose a 98% confidence interval for u turns out to be (1,000 , 2100). If this interval was based on a sample of size n=22, explain what assumptions are necessary for this interval to be valid.
A population has a standard deviation of 10. If a sample of size 25 is selected from this population, what is the probability that the sample mean will be within ±2 of the population mean?
Nicola, Stephanie, Kathryn, and William, in that order, take turns at rolling a fair die until one of them throws a 6. What is the probability that William is the first to throw a 6?
A teacher finds the distribution of scores on a final exam to be positively skewed with low variability. On the basis of this information, the teacher would be most justified in concluding that
What is the most likely shape for a distribution with a mean of 20 and a mode of 25? Group of answer choices Negatively skewed Positively skewed Symmetrical Either positively or negatively skewed
The shape of the sampling distribution of ¯¯¯xx¯ is approximately Normal when the sample size is _____ even when the population shape is not-Normal. (Assume finite population standard deviation.)
A linear trend model estimated from 50 days of data is given by ŷ = 85.20 + 0.68t. Use the estimated model to forecast y for the next two days. Note: Round your answers to 2 decimal places.
Determine the margin of error for a confidence interval to estimate the population proportion for the following confidence levels with a sample proportion equal to 0.34 and n equals 100.
What would be the semi-interquartile range of data in population B? Rats Score Rats Score 1A 22 1B 70 2A 36 2B 47 3A 30 3B 62 4A 44 4B 59 5A 47 5B 38 a. 7.5 b. 17.75 c. 22.75 d. 11.5
(a) Find the area above 27 for a distribution. Round your answer to three decimal places. Area = (b) Find the area below 11 for a distribution. Round your answer to three decimal places. Area =
The results from an independent-measures t hypothesis test are reported as “t(14) = 2.13,p > .05, two tailed.”For this test, the null hypothesis was rejected. Group of answer choices True False
A standard deck of cards has 4 suits (hearts, spades, diamonds, and clubs), each with 13 cards. How many five card poker hands are flushes? (A flush consists of all cards from the same suit.
Use the range rule of thumb to find the minimum and maximum usual number of adults in favor of funding new government programs to help create jobs in a random sample of 10 adults. (5pts)
Question 9 Let Y1, Y2, . . . , Yn denote a random sample from the probability density function fY (y|θ) = ( (θ + 1)y θ , 0 < y < 1, θ > −1 0, otherwise (5) Find the MLE of θ. [1.5 marks]
A quiz consists of 11 multiple choice questions, each with 4 answer choices. If a student guesses kn each question, What is the probability that he/she will answer 2 questions correctly?
On average, a person spends 4.3 hours in the beach. There are on average 360 people in the beach. On average, how many people enter the beach every hour? Note: Round your answer to 2 decimals.
A sample of 51 observations will be taken from an infinite population. The population proportion equals 0.15. The probability that the sample proportion will be less than 0.235 is _____.
A study of 33,680 dairy cows found that the mean milk yield was 13.8 kg per milking with a standard deviation of 5.6 kg per milking a cow produces 17.6 kg per milking. What is the cows Z score
Seven digits from 1, 2, 3, 4, 5, 6, 7 are chosen and arranged in a row without replacement to form a 7-digit number. Find the probability that the resulting number is divisible by 4
Find 𝑃𝑃[𝐾𝐾 < 𝐸𝐸[𝐾𝐾]] when a. 𝐾𝐾 is geometric (1/3). (3 pts) b. 𝐾𝐾 is binomial (6, 1/2). (3 pts) c. 𝐾𝐾 is Poisson (3). (3 pts) d. 𝐾𝐾 is discrete uniform (0, 6).
A student visits a population of five local restaurants (N = 5) and rates each as follows: 4, 3, 6, 4, and 8. What is the standard deviation of the population? a. 1.79 b. 1.94 c. 2 d. 1.84
If X follows a Poisson distribution with a standard deviation of 9, what is the expected value of X? 09 0 25 81 There is not enough information given to find the expected value of X. 0 49
You order 10 different books online, 3 of which are for your sister. The books arrive randomly, one by one. What is the probability that the books for your sister arrive consecutively?
Let X and Y have a bivariate normal distribution with μX = 70, σ2 X = 100, μY = 80, σ2 Y = 169, and ρ = 5/13. Find (a) E(Y | X = 72). (b) Var(Y | X = 72). (c) P(Y ≤ 84, | X = 72).
The population distribution of scores on a test is normal with μ = 40 and σ = 2. What is the probability of scoring less than a 38 on this test? a. 2.28% b. 13.59% c. 15.87% d. 34.13%
A bin contains 71 light bulbs of which 7 are defective. If 3 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones.
A random sample of size 100 is taken from a population where the population proportion p = 0.60. The probability that the sample proportion is greater than 0.62 is __________blank.
Use the given data to construct a 90% confidence interval for the population proportion p . =x51, =n72 Round the answer to at least three decimal places. Theconfidenceintervalis, .
Let X be an exponential random variable with expectation 1. Find the density of Y := X2 and compute the probabilities – P(Y ≥ 1 + t|Y ≥ t) – P(X ≥ 1 + t|X ≥ t) for every t > 0
Using the results you got from Question 3 and a level of significance of .05, what are the two-tailed critical values associated with each result? Would the null hypothesis be rejected?
Suppose X and Y are random variables such that the standard deviation of X is 2 andthe standard deviation of Y is 5. Consider a random variable Z defined as:Z = 3X2Y 5 Not independent
In a certain study, the chances of encountering a car crash on the road are stated as 19 out of 100. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive
If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then the probability that either A or B occur is a. 0.10. b. 0.12. c. 0.70. d. none of these choices.
An analysis of variance produces SStotal = 80 and SSwithin = 30. For this analysis, what is SSbetween? Group of answer choices 50 Cannot be determined without additional information 110 30
If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur? a. 0.0 b. 0.5 c. 1.0 d. This can be any probability between 0 and 1.
repeat question one without assuming that the standard deviation is known to be 0.4. in other words estimate the population variance from the sample measurements and use the t-test
The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 21 minutes. What is the probability that washing dishes will take me between 18 and 19 minutes
In an analysis of variance problem involving 4 treatments and 11 observations per treatment, SSE = 339.6. Find the MSE for this situation. Group of answer choices 7.72 84.90 8.49 30.87
If two states are selected at random from a group of 1010 states, determine the number of possible outcomes if the group of states are selected with replacement or without replacement.
If six people are randomly selected off the street, what is the probability that at least two of them have the same birthday? Question 8 options: 0.0105 0.0205 0.0305 0.0405 0.0505
If two values are independently sampled from the standard normal distribution, what is the probability they are both less than 2.13? Round your answer to two decimal places, i.e., 0.12.
A recent study shows that 30% of all adults in the US played tennis at least once last year. If you survey 9 random adults, what is the probability that less than 3 played tennis?
To determine the number of deer in a forest, a naturalist catches, tags, and releases 117 deer. Later, 30 deer are caught, and 27 have tags. Estimate the number of deer in the forest.
Suppose that the number of accidents occurring on a highway each day is a Poisson random variable with expectation 3. Find the probability that more than 2 accidents occur today
It is estimated that 93 % of senior citizens suffer from sleep disorders and 8 % suffer from anxiety. Moreover, 5 % of senior citizens suffer from both sleep disorders and anxiety.
A lumber mill receives a shipment of 65,500 cubic feet of wood. The supervisor estimates that 61,000 cubic feet of the wood is clear (meaning free of defects). What percentage is this?
Two students each use a random number generator to pick an integer between 6 and 13 inclusive. What is the probability that they pick the same number? (Enter your answer as a fraction.)
Match the p-values with the appropriate conclusion: I. 0.00009 II. 0.0363 III.0.0869 IV. 0.4026. (a) The evidence against the null hypothesis is significant, but only at the 10% level
The amount of time, in minutes, that a person must wait for a bus is uniformly dsitributed between 0 and 23 minutes. What is the probability that a person waits more than 12 minutes?
If two events are mutually exclusive, what is the probability that one or the other occurs? a. 0.25 b. 0.50 c. 1.00 d. This cannot be determined from the information given.
This statistical test examines the relationship between two sets of variables to determine whether they are associated or not. Group of answer choices ANOVA Pearson r Chi-square t-Test
State the null and alternative hypotheses for the situation described below for a statistical test. Testing to see if average sales are higher in stores where customers are approached
THE AAA reports that of the fatal car accidents, 54% are caused by driver error. If 3 accidents are chosen at random, find the probability that at least 1 is caused by driver error?
If the class mid points in a frequency distribution of age of a group of persons are 25, 32, 39, 46, 53 and 60. The size of class interval is: Question 37 options: A. 5 B. 7 C. 8 D. 6
Suppose that the two random variables X and Y have an exact linear relationship:Y= a bX where a and b are constants. What is the correlation coefficient (X,Y )between X and Y ?
A stoplight just turned red. The probability that a light turns green in the next x minutes is given by the  function f below where k is a constant.  f(x) =  kcos π 2x 1
Suppose that the true population mean is 52.1 and the true population standard deviation is 19.3. If you draw a sample of size 36 then the z value for a sample mean of 59.9 is what?
[STOP3A] Compare the 95% with the 99% confidence interval for the population mean, which is wider? Need to know the standard deviation. Need to know the standard error. 95% 99%
With case control studies, epidemiologists identify a group of subjects with particular outcomes and compare them to a group without the conditions. Group of answer choices True False
What is the probability that, for five girls and three boys standing in a line: a) All three boys are standing together. b) No two boys are standing next to each other
For a population with a standard deviation of σ = 5, what is the z-score corresponding to a score that is 15 points above the mean? Group of answer choices z = 3 z = 12 z = 5 z = 1
ompute the following probabilities: a) If and B, find or B. b) If P(A)=0.57,P(B)=0.35, and A and B are mutually exclusive, find or B. c) Let P(A)=0.4,P(B)=0.8. Assume that A
Blue Star Optical is conducting a satisfaction survey of its 10,000 customers. There will be 100 customers in the final sample. How would the company pull a systematic sample of 100?
The working lifetime, in years, of a particular model of client is normally distributed with mean 10 and variance 4. Calculate the 14th percentile of the working lifetime, in years.
Let X be a normal random variable with mean μ = 77.523 and standard deviation σ = 2.897, find the value x such that P (X > x) = 0.7967. Enter your answer in Akindi line 16
Chao is assessing the percentage of customers who have not returned to the Fruit-of-the-Month Club to estimate how many might leave on a yearly basis. What process is Chao working on?
In this exercise, test H0:p1=p2 vs Ha:p1>p2, with p1-p2 =0.8 -07 =0.10 for different sample sizes. In parts (a) and (b), use StatKey or other technology to find the p-value.
A researcher conducted a one way between subjects ANOVA and found a significant analysis result but decided to retain the null hypothesis. Should they report the effect size?
The amount of time, in minutes, that a person must wait for a bus is uniformly distrubuted between 0 and 23 minutes. What us the probability that a person waits more than 8 minutes
Consider the variable Sale Condition. It is Quantitative or Qualitative? Quantitative Qualitative Neither Quantitative nor Qualitative Not enough information to determine the answer
Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 X 90) is a. 0.5328. b. 0.3413. c. 0.1915. d. 0.1498.
The amount of time in minutes that a person must wait for a bus is uniformly distributed between 0 and 23 minutes. What is the probablity that a persoj waite more than 8 minutes.
If one sample has n = 10 scores with SS = 15 and a second sample has n = 10 scores with SS = 30, then the pooled variance will be _____. Group of answer choices 2.50 .75 2.25 1.50
What is the confidence level (written as a percentage) for the interval x̅-2.14 σ / √(n)≤μ≤x̅+2.14 σ / √(n) ? (Round your answer to 2 decimal places.) 8 Attempts: 0 of 1 used
Let X1 be a number selected randomly from the set {0, 10−3, 103} and let X2 be independent of X1 identically distributed. Let Y = X1X2. Compute E[X2|Y ̸ = 0].
Someone flips 15 biased coins once. The coins are weighted such that the probability of a head with any coin flip is .85 (P = .85). What is the probability of getting
Which of the following is a proper way to describe the probability of flipping heads on a fair coin? I. ½ II. 0.5 III. 50% a. I only b. III only c. I and III only d. I, II, and III
What is the confidence level (written as a percentage) for the interval x̅-2.49 σ / √(n)≤μ≤x̅+2.49 σ / √(n) ? (Round your answer to 2 decimal places.) 8 Attempts: 0 of 1 used
An assumption of ANOVA is that 1. all groups have the same variance 2. all groups are from Normal populations 3. all observations are independent 4. all of the above (1, 2, and 3)
For each of the following measures, give the value that implies no difference between the two groups being compared. (a) relative risk (b) odds ratio (c) percent increase in risk %
Can you use the confidence interval you constructed in part (a) to test the hypotheses H0 : µ = 11 versus Ha : µ ̸= 11 at 1% significance level? Briefly explain without a P-value.
A polling organization conducts a poll by making a random survey and is willing to accept a margin of error of 4% at a confidence level of 95%. What should the sample size be?
a judge is 63% sure that a suspect has committed a crime. during the course of a trial a witness convinces the judge that there is an 81% chance that the criminal is left handed
Consider a normal population distribution with the value of 𝜎 known. (a) What is the confidence level for the interval x ± 2.88𝜎⁄ n ? (Round your answer to one decimal place.)
If a coin is flipped 4 times, what is the probability of getting exactly 3 heads, given that at least 1 head is obtained? Question 5 options: 0.392 0.441 0.267 0.412 0.357
. A fair coin is tossed twice. Let X represent the number of heads obtained on the firsttoss and Y represent the total number of heads obtained in two tosses.
Market share turns out to be a strong, positive predictor of the company’s future customer satisfaction, because consumers prefer many choices in the market place. True or False?
If the probability then in the event will occur 1/3 and the probability that the event will not occur is 2/3 in the eyes in favor of the event occurring are simplify your answer
Suppose x has a normal distribution with mean 𝜇 = 29 and standard deviation 𝜎 = 4. Describe the distribution of x values for sample size n = 4. (Round 𝜎x to two decimal places.)
Two fair six-sided dice are rolled (one maize and one blue), with outcomes 𝑋 and 𝑌 respectively for the maize and the blue. (b) Are X + Y and X − Y independent? Explain.
A set of n = 4 scores has a mean of μ = 11. If 8 points are subtracted from one of the scores, what is the new value for the population mean? Group of answer choices 11 9 10 13
A study finds a correlation coefficient of r = .52. According to Cohen’s benchmarks, the magnitude of this effect is: a. multiply determined. b. categorical. c. large. d. modest.
Samples of size n = 9 are selected from a population with μ = 60 with σ = 20. What is the expected value for the distribution of sample means? Group of answer choices 60 80/3 6 18
Which is not an assumption for residuals in multiple regression? Group of answer choices Normally distributed Heteroskedasticity mean = 0 Variance is the same at all values of X
A normal population has a mean of $62 and standard deviation of $14. You select random samples of nine. What is the probability that a sample mean is between $58 and $65?
Suppose X and Y are random variables such that the standard deviation of X is 2 andthe standard deviation of Y is 5. Consider a random variable Z defined as:Z = 3X2Y 5
suppose that the life of a lightbulb, x, in thousands of hours is exponentially distributed random variable (one failure every 10,000 hours on average) compute p(X>12 | X>10)
What is the minimum sample size that would be needed to ensure that the length of the CI in part (a) is 0.5 µg/mL assuming the sample standard deviation remains at 2.0 µg/mL?
The obtained chi-square is 2512. Based on alpha of 0, what can you conclude about the relationship between gender and views on restoring the voting rights of felons in prison?
Determine if each event is independent or dependent. A green die and a red die are tossed. What is the probability that a 4 shows on the green die and a 5 shows on the red die?
If the moment-generating function of X is M(t) = exp(166t + 2007}), -00 < 1 < 00, find (a) The mean of X. (c) P(170 < X < 200). (b) The variance of X. (d) P(148 ≤ X ≤ 172).
A normal population has a mean of $61 and standard deviation of $13. You select random samples of nine. What is the probability that a sample mean is greater than $64?
If an analysis of variance is used for the following data, what would be the effect of changing the value of M1 to 20? Sample Data M1 = 15 , M2 = 10 SS1 = 90 , SS2 = 70
A normal population has a mean of $62 and standard deviation of $14. You select random samples of nine. What is the standard error of the sampling distribution of sample means?
Prove that for a two-variable regression model R 2 = r 2 where R is the coefficient of determination and r is the coefficient of correlation between X and Y.
The formula used to calculate a large-sample confidence interval for p is... What is the appropriate z critical value for each of the following confidence levels? 80% and 94%
A normal population has a mean of $60 and standard deviation of $12. You select random samples of nine. What is the standard error of the sampling distribution of sample means?
A normal distribution has a mean of u=70 and o=10. If one score is randomly selected from this distribution what is the probability that the score will be greater than x =82
A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. The probability that the sample mean is less than 15 is __________blank.
Which of the following sets of data has an interquartile range of 10 ? 12,14,17,19,19,20,21 55,56,56,57,58,59,62 41,43,49,49,50,53,55 3.4 .9 .16 .17 .24 .31
A researcher is conducted a study and finds degrees of freedom equal to (3,36). What will be the critical value of a one way between subjects ANKVA at .05 level of significance
A normal population has a mean of $60 and standard deviation of $12. You select random samples of nine. What is the probability that a sample mean is between $56 and $63?
A sample of n = 16 scores has a standard error of 4. What is the standard deviation of the population from which the sample was obtained? Group of answer choices 64 2 4 16
A study found that in blue collar jobs, with similar qualifications and general appearance, African Americans were offered jobs at about 50% the rate of Latinos. True or False
Would the margin of error for a 95% confidence interval increase or decrease if we increased the sample size to 600 (assume the value of is the same as part (c))? Why?(2 pts)
Wechsler classifies "visual-motor coordination" as a _______________________________. Group of answer choices Verbal Test Performance Test General Test Intelligence Test Next
A sample of 240 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 15. Determine the standard error of the mean.
Tourists enter a museum at the rate of 0.4 tourists per second. There are, on average, 5,600 tourists in the museum. On average, how long does a tourist spend in the museum?
Would belief in the law of small numbers lead people to think that the two events in part (b) are equally likely, or are not equally likely? Would they be correct? Explain.
A population of plant heights has a mean of μ = 13 and standard deviation of σ = 2. What is the probability of an individual plant having a height between 10 and 16? a. 13.36% b. 68.27% c. 86.64% d. 93.32%
A research assistant determines they will need to randomly assign 20 participants to one of three groups. If they were to compute a one way between subjects ANOVA what would be the degrees of freedom within groups?
If X is χ^2(23), find the following: (a) P(14.85 < X < 32.01). (b) Constants a and b such that P(a < X < b) = .95 and P(X < a) = .025. (c) The mean and variance of X. (d) (χ^2)_.05(23) and (χ^2)_.95(23).
Refer to the probability density function given: fX(x) = e −(x−β) , x > β > 0 a) Find a method of moments estimator (MoM) for β [1 mark] b) Find a maximum likelihood estimator (MLE) for β [1 mark]
Develop a three-week moving average for this time series. Compute MSE and a forecast for week 8.If required, round your answers to two decimal places. Do not round intermediate calculation.
According to Harper's Index, 40% of all federal inmates are serving time for drug dealing. A random sample of 20 federal inmates is selected. What is the probability that 5 or fewer are serving time
A fair six-sided die is rolled 180 times. What is the probability that the “3” is rolled exactly 35 times? find the approximate probability using the normal distribution without continuity correction
What is the SS, sample variance, and standard deviation of class B? Class A Time Class B Time 1 39 1 48 2 42 2 36 3 49 3 40 4 56 4 41 5 69 5 45 6 61 6 37 7 37 7 39 8 31 8 30 9 45 9 49 10 53 10 36
Circle of radius r has area A = πr2. If a random circle has a radius that is uniformly dis- tributed on the interval (0, 1), what are the mean and variance of the area of the circle?
Based on past results, there is a 0.008 probability of finding bacteria in the swimming piil area. Find the probability that a combined sample from two public swimming areas will reveal the presence of bacteria
If Z is a standard normal random variable (that is, has mean zero and standard deviation 1), what is the probability that Z is between -2 and 2, that is, what is P( -2 < Z < 2), rounded to 3 decimal places.
During the season, Charlotte's team scored the following total points for 6 games: 92 points, 95 points, 95 points, 101 points, 112 points, and 143 points. Calculate the range for the points Charlotte's team scored.
If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of two successes in 15 trials, the correct probability function to use is the _____.
Suppose the correlation between height and weight for adults is +0.80. What proportion of the variability in weight can be explained by the relationship with height? Question 20 options: A. 20% B. 36% C. 64% D. 80%
If 15% of adults in a certain country work from home, what is the probability that fewer than 60 out of a random sample of 500 adults will work from home? (Round your answer to 4 decimal places) Incorrect
In a large general education class, 40% (0.4) are science majors, and 60% (0.6) are liberal arts majors. Ten percent (0.1) of the science majors are seniors, while 50% (0.5) of the liberal arts majors are seniors.
Jonas gets a 92% on Exam 1, a 65% on Exam 2, a 89% on Exam 3, and a 95% on Exam 4. What is his average exam score (assuming all exams are weighted equally)? His average score is: _______ % (do not round your answer
of a kịnd." B. SCOPE OF PSYCHOLOGY Psychology as a discipline or branch of knowledge has it's own scope of study. Basically it studies human experiences and behaviour. It primarily looks into the factors that
Four students are running for class president: Liz, Sam, Sue, and Tom. The probabilities of Sam, Sue, and Tom winning are 1⁄4 , 1⁄10 and 3⁄20 , respectively. What is the probability that Tom loses?
A student visits a population of five local restaurants (N = 5) and rates each as follows: 4, 3, 6, 4, and 8. Using the computational formula, what is the SS and σ2? a. 17; 3.4 b. 20; 4 c. 18; 3.6 d. 16; 3.2
The mean of women’s heights is 63.5 inches and the standard deviation is 2.5 inches. Select the two heights that define the lower and upper bounds of a range that encompasses about 99.7% of all women’s heights.
The probability that any one customer purchases a product warranty is 0.4. What is the probability that exactly 4 customers out of the next 10 will purchase a warranty? Answer to four decimal places.
Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy. (a)Mean absolute errorIf required, round your answer to one decimal place.
Consider a binomial experiment with n=20 and p=0.70. a. Compute f(12) (to 4 decimals). b. Compute f(16) (to 4 decimals). c. ComputeP(x>or equal to 16) (to 4 decimals). d. Compute P(x
suppose the time spent by a randomly selected student who uses a terminal connected to a local time sharing computer facility has a gamma distribution with mean 20 min and then variance 80 min, what are
The set of values of the statistic so obtained, one for each sample, constitutes what is called: Question 48 options: A. Sampling distribution B. Systematic sampling C. Stratified sampling D. Cluster sampling
onas gets a 92% on Exam 1, a 65% on Exam 2, a 89% on Exam 3, and a 95% on Exam 4. What is his average exam score (assuming all exams are weighted equally)? His average score is: _______ % (do not round your answer
Let X1, X2 be iid N(θ,1) (0 ≤ θ ≤ 1) and define the following decision rules: δ1 = 1 2 X1 + 1 2 X2; δ2 = 1 4 X1 + 3 4 X2; δ3 = 2 3 X1; and δ4 = 2 3 δ1. Consider squared error loss.
A certain drug causes liver damage in 50 % of patients. Suppose the drug is to be tested on 100 patients. How many patients would we expect to see with liver damage following use of the drug?    
It will be convenient to do a telephone survey in rural areas in China since, according to the Ministry of Information Industry reports, 40 percent of households have at least one fixed-line telephone. True False
suppose the first year salaries of uhcl graduates is normally distributed with a mean of 55000 also 7% uhcl graduates have first year salaries greater than $106000 what should be the standard deviation?
Box 1 contains 5 Red and 3 Black balls. Box 2 contains 3 Red and 1 Black ball. Box 3 contains 4 Red and 2 Black balls. If a Box is selected at random and a ball is drawn, find the probability it will be Red?
One study involving heavy use of phones showed the mean of the battery life to be 11.25 hours with a standard deviation of 2.2hours. Find the probability that with heavy use the life exceeds 12 hours
The alternative hypothesis is: the average amount of money spent at the PSU Bookstore is less than $100. We are using a significance level of 0.05. The Z statistic is 1.70. What’s the correct conclusion?
In a recent poll, 100 people were asked if they liked broccoli, and 69% said they did. Based on this, construct a 90% confidence interval for the true population proportion of people who like broccoli.
Find the moment-generating function for the gamma distribution with parameters a and e. HINT: In the integral representing E(e'*), change vari- ables by letting y = (1 - 0f)x/e, where 1 - 0t > 0.
The round off error when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5 mm. Round all answers to one decimal place, where your answer is not a whole number.
If Z is N(0,1) find (a) P(.47 < Z ≤ 2.13). (b) P(-.97 ≤ Z < 1.27). (c) P(Z > -1.56). (d) P(Z > 2.78). (e) P(|Z| < 1.96). (f) P(|Z| < 1). (g) P(|Z| < 2). (h) P(|Z| < 3).
For the given confidence level and values of x and n , find the following. =x44 , =n99 , confidence level 99.8% Find the standard error. Round the answers to at least four decimal places, if necessary.
to estimate the proportion of teen traffic deaths in Texas last year that was caused by speeding, determine the necessary sample size for the estimate to be accurate to within .05 with confidence .99
A local news agency is interested in studying unemployment rates across the state. The researchers will randomly select 1000 people from each state county and gather all relevant data from those selected.
GRADES 7What is the final conclusion? Select the BEST option for each blank.We[ Select ]the nullhypothesis because the P-value is less than or equal to the 5% significance level. We therefore[ Select ]that
In a classroom there are 105 students. 58 of them are male. There are 49 seniors in the class and 28 of the females are seniors. What is the probability that a randomly chosen student is a male and a senior
(d) On the basis of clinical trials, the probability of efficacy of a new drug is 0.760. A. Subjective method B. Classical method C. Empirical method D. It is impossible to determine which method is used.
Consider the following game. You pick a card from a deck and each time you select an ace, you get $260. For all other cards you must pay $13. What is the expected value of the game? $32 -$12 $0 $8
A professor analyzes two sets of student test scores. Class A has a mean of 75 and a standard deviation of 10, while Class B has a mean of 80 and a standard deviation of 20. Which statement is correct?
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 88 minutes and a maximum of 100 minutes. What is the probability that a flight is between 89 and 91 minutes?
A population consists of 8 items. The number of different simple random samples of size 3 (without replacement) that can be selected from this population is _____. Question 23 options: 24 56 512 128
a box contains 5 red and 7 blue balls. draw 6 balls with replacement. let u denote the variable equal to the number of red balls drawn. calculate the probability you get at most 3 red balls
A chi-square test for goodness of fit has df = 2. How many categories were used to classify the individuals in the sample? Group of answer choices 2 3 4 Cannot be determined without additional information
Given a standard normal distribution, find the value of k such that P(k < Z < −0.18) = 0.4197. Hint: Find area (pnorm) to the left of -0.18, subtract 0.4197 from it, find k (qnorm) of this difference.
It is construction season, and Google maps lists five different routes to your job. The travel times (in minutes) are: 21, 28, 14, 15, and 12. Calculate the population variance in route travel times.
A study finds a correlation coefficient of r = .52 and reports p < .05. The p is a _________. a. plausible significance approximation b. population value c. possibility assessment d. probability estimate
If the probability that an event will occur is three elevenths311, then the probability that the event will not occur is eight elevenths811, and the odds in favor of the event occurring are ________.
Find the probability that the sample mean is more than $75,000. Report your answer to 4 decimal places. If this is a probability that cannot be determined, then state unknown as your answer.
A sample of 240 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 15. Determine the 99% confidence interval for the population mean.
A population of birth weights has a mean of μ = 8.1 and a standard deviation of σ = 0.1. What is the probability of an individual weight being greater than 8.4? a. 99.87% b. 15.87% c. 2.28% d. 0.13%
a. Construct a 9999% confidence interval to estimate the actual proportion of students enrolled in college or a trade school within 1212 months of graduating from high school in 20172017.
9) A Rasmussen Reports survey of a random sample of 1,000 US adults found that 43% believe it will help the economy. Conduct an appropriate hypothesis test to help answer the research question
When pulling a single card out of a well-shuffled deck, which card demonstrates that the events {Face card} and {Spade} are not disjoint? King of Clubs Ace of Spades Queen of Spades The Ten of Hearts
Let X and Y be continuous random variables with the following joint density function: f(x, y) = 3 4 (2 − x − y) for 0 < x < 2, 0 < y < 2, x + y < 2 0 otherwise Compute E[X | Y < 1]
What is a typical eye blink rate for an infant about 2 to 3 months old? Group of answer choices mopre than 10 blinks per minute ~ 7 to 8 blinks per minute ~1 blink per minute ~2 to 3 blinks per minute
Interpreting a P-value. In each case, indicate whether the statement is a proper interpretation of what a p-value measures. The probability of make a Type 1 error, if the null hypothesis, H0 is true.
A simple random sample of 12 observations is derived from a normally distributed population with a population standard deviation of 4.2. Is the condition that X⎯⎯⎯X¯ is normally distributed satisfied?
From a population of 200 elements, the standard deviation is known to be 24. A sample of 64 elements is selected. It is determined that the sample mean is 57. The standard error of the mean is _____.
What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.) 98% confidence, n = 24 90% confidence, n = 24
What is the minimum sample size is required to estimate a population mean with 90% confidence when the desired marginal bear is D equals 1.25 the standard deviation and a pre-selected samples 8.5
The average score for games played in the nfl is 21.8 and the standard deviation is 9.1 points. 17 games are randomly selected. Find the 15th percentile for the mean score for this sample size.
The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 23 minutes, inclusive. What is the probability that a person waits fewer than 8 minutes?
If x follows a Poisson distribution with a standard deviation of 7, what is the expected value of X? A) 49 B) there is not enough information given to find the expected value of X C) 25 D) 81 E) 9
The basic objective of a sample is to draw ____________________ about the population from which such sample is drawn. Question 49 options: A. Conclusion B. Characteristics C. Inferences D. Parameters
If 15% of adults in a certain country work from home, what is the probability that fewer than 48 out of a random sample of 400 adults will work from home? (Round your answer to 4 decimal places)
If people adopted healthy lifestyle behaviors such as regular exercise and a moderate diet, about ________ of cases of type 2 diabetes could be prevented. Question 8Answer a. 90% b. 70% c. 80% d. 60%
Given a confidence level value C (in decimals), the significance level α for a population with mean μ can be determined using the formula: Group of answer choices α = 1/C α = μ/C α = 1 - C α = μ - C
Someone flips 15 biased coins once. The coins are weighted such that the probability of a head with any coin flip is .85 (P = .85). What is the probability of getting at least 14 heads
Determine the margin of error for a confidence interval to estimate the population proportion for the following confidence levels with a sample proportion equal to 0.340.34 and nequals=100100.
The mean score of a placement exam for entrance into a manta class is 80, with a standard deviation for 10. Use the empirical rule to find the percentage of scores that lie between 60 and 80.
If X is a random variable having a Binomial distribution with parameters n and 𝜃, show that U = '(! $(" is a biased estimator of 𝜃. Is U an asymptotically unbiased estimator of 𝜃? Justify
Whats the probability of picking two Queens from a deck of cards without replacement? Pick the correct formula. ((4)/(52))((3)/(51)) ((4)/(52))((4)/(51)) ((4)/(52))((3)/(52)) ((2)/(52))((3)/(51))
determine whether or not there is a significant relationship between number of full-time jobs added and the two independent variables (full time voluntary turnover and total worldwide revenue)
How large a sample should be taken if the desired margin of error is $400? Use a rounded z value (2 decimals) in your calculations .Round your answer for n to next whole number. $170?
Suppose a 98% confidence interval for u turns out to be (1,000 , 2100). If this interval was based on a sample of size n=22, explain what assumptions are necessary for this interval to be valid.
A population has a standard deviation of 10. If a sample of size 25 is selected from this population, what is the probability that the sample mean will be within ±2 of the population mean?
Nicola, Stephanie, Kathryn, and William, in that order, take turns at rolling a fair die until one of them throws a 6. What is the probability that William is the first to throw a 6?
A teacher finds the distribution of scores on a final exam to be positively skewed with low variability. On the basis of this information, the teacher would be most justified in concluding that
What is the most likely shape for a distribution with a mean of 20 and a mode of 25? Group of answer choices Negatively skewed Positively skewed Symmetrical Either positively or negatively skewed
The shape of the sampling distribution of ¯¯¯xx¯ is approximately Normal when the sample size is _____ even when the population shape is not-Normal. (Assume finite population standard deviation.)
A linear trend model estimated from 50 days of data is given by ŷ = 85.20 + 0.68t. Use the estimated model to forecast y for the next two days. Note: Round your answers to 2 decimal places.
Determine the margin of error for a confidence interval to estimate the population proportion for the following confidence levels with a sample proportion equal to 0.34 and n equals 100.
What would be the semi-interquartile range of data in population B? Rats Score Rats Score 1A 22 1B 70 2A 36 2B 47 3A 30 3B 62 4A 44 4B 59 5A 47 5B 38 a. 7.5 b. 17.75 c. 22.75 d. 11.5
(a) Find the area above 27 for a distribution. Round your answer to three decimal places. Area = (b) Find the area below 11 for a distribution. Round your answer to three decimal places. Area =
The results from an independent-measures t hypothesis test are reported as “t(14) = 2.13,p > .05, two tailed.”For this test, the null hypothesis was rejected. Group of answer choices True False
A standard deck of cards has 4 suits (hearts, spades, diamonds, and clubs), each with 13 cards. How many five card poker hands are flushes? (A flush consists of all cards from the same suit.
Use the range rule of thumb to find the minimum and maximum usual number of adults in favor of funding new government programs to help create jobs in a random sample of 10 adults. (5pts)
Question 9 Let Y1, Y2, . . . , Yn denote a random sample from the probability density function fY (y|θ) = ( (θ + 1)y θ , 0 < y < 1, θ > −1 0, otherwise (5) Find the MLE of θ. [1.5 marks]
A quiz consists of 11 multiple choice questions, each with 4 answer choices. If a student guesses kn each question, What is the probability that he/she will answer 2 questions correctly?
On average, a person spends 4.3 hours in the beach. There are on average 360 people in the beach. On average, how many people enter the beach every hour? Note: Round your answer to 2 decimals.
A sample of 51 observations will be taken from an infinite population. The population proportion equals 0.15. The probability that the sample proportion will be less than 0.235 is _____.
A study of 33,680 dairy cows found that the mean milk yield was 13.8 kg per milking with a standard deviation of 5.6 kg per milking a cow produces 17.6 kg per milking. What is the cows Z score
Seven digits from 1, 2, 3, 4, 5, 6, 7 are chosen and arranged in a row without replacement to form a 7-digit number. Find the probability that the resulting number is divisible by 4
Find 𝑃𝑃[𝐾𝐾 < 𝐸𝐸[𝐾𝐾]] when a. 𝐾𝐾 is geometric (1/3). (3 pts) b. 𝐾𝐾 is binomial (6, 1/2). (3 pts) c. 𝐾𝐾 is Poisson (3). (3 pts) d. 𝐾𝐾 is discrete uniform (0, 6).
A student visits a population of five local restaurants (N = 5) and rates each as follows: 4, 3, 6, 4, and 8. What is the standard deviation of the population? a. 1.79 b. 1.94 c. 2 d. 1.84
If X follows a Poisson distribution with a standard deviation of 9, what is the expected value of X? 09 0 25 81 There is not enough information given to find the expected value of X. 0 49
You order 10 different books online, 3 of which are for your sister. The books arrive randomly, one by one. What is the probability that the books for your sister arrive consecutively?
Let X and Y have a bivariate normal distribution with μX = 70, σ2 X = 100, μY = 80, σ2 Y = 169, and ρ = 5/13. Find (a) E(Y | X = 72). (b) Var(Y | X = 72). (c) P(Y ≤ 84, | X = 72).
The population distribution of scores on a test is normal with μ = 40 and σ = 2. What is the probability of scoring less than a 38 on this test? a. 2.28% b. 13.59% c. 15.87% d. 34.13%
A bin contains 71 light bulbs of which 7 are defective. If 3 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones.
A random sample of size 100 is taken from a population where the population proportion p = 0.60. The probability that the sample proportion is greater than 0.62 is __________blank.
Use the given data to construct a 90% confidence interval for the population proportion p . =x51, =n72 Round the answer to at least three decimal places. Theconfidenceintervalis, .
Let X be an exponential random variable with expectation 1. Find the density of Y := X2 and compute the probabilities – P(Y ≥ 1 + t|Y ≥ t) – P(X ≥ 1 + t|X ≥ t) for every t > 0
Using the results you got from Question 3 and a level of significance of .05, what are the two-tailed critical values associated with each result? Would the null hypothesis be rejected?
Suppose X and Y are random variables such that the standard deviation of X is 2 andthe standard deviation of Y is 5. Consider a random variable Z defined as:Z = 3X2Y 5 Not independent
In a certain study, the chances of encountering a car crash on the road are stated as 19 out of 100. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive
If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then the probability that either A or B occur is a. 0.10. b. 0.12. c. 0.70. d. none of these choices.
An analysis of variance produces SStotal = 80 and SSwithin = 30. For this analysis, what is SSbetween? Group of answer choices 50 Cannot be determined without additional information 110 30
If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur? a. 0.0 b. 0.5 c. 1.0 d. This can be any probability between 0 and 1.
repeat question one without assuming that the standard deviation is known to be 0.4. in other words estimate the population variance from the sample measurements and use the t-test
The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 21 minutes. What is the probability that washing dishes will take me between 18 and 19 minutes
In an analysis of variance problem involving 4 treatments and 11 observations per treatment, SSE = 339.6. Find the MSE for this situation. Group of answer choices 7.72 84.90 8.49 30.87
If two states are selected at random from a group of 1010 states, determine the number of possible outcomes if the group of states are selected with replacement or without replacement.
If six people are randomly selected off the street, what is the probability that at least two of them have the same birthday? Question 8 options: 0.0105 0.0205 0.0305 0.0405 0.0505
If two values are independently sampled from the standard normal distribution, what is the probability they are both less than 2.13? Round your answer to two decimal places, i.e., 0.12.
A recent study shows that 30% of all adults in the US played tennis at least once last year. If you survey 9 random adults, what is the probability that less than 3 played tennis?
To determine the number of deer in a forest, a naturalist catches, tags, and releases 117 deer. Later, 30 deer are caught, and 27 have tags. Estimate the number of deer in the forest.
Suppose that the number of accidents occurring on a highway each day is a Poisson random variable with expectation 3. Find the probability that more than 2 accidents occur today
It is estimated that 93 % of senior citizens suffer from sleep disorders and 8 % suffer from anxiety. Moreover, 5 % of senior citizens suffer from both sleep disorders and anxiety.
A lumber mill receives a shipment of 65,500 cubic feet of wood. The supervisor estimates that 61,000 cubic feet of the wood is clear (meaning free of defects). What percentage is this?
Two students each use a random number generator to pick an integer between 6 and 13 inclusive. What is the probability that they pick the same number? (Enter your answer as a fraction.)
Match the p-values with the appropriate conclusion: I. 0.00009 II. 0.0363 III.0.0869 IV. 0.4026. (a) The evidence against the null hypothesis is significant, but only at the 10% level
The amount of time, in minutes, that a person must wait for a bus is uniformly dsitributed between 0 and 23 minutes. What is the probability that a person waits more than 12 minutes?
If two events are mutually exclusive, what is the probability that one or the other occurs? a. 0.25 b. 0.50 c. 1.00 d. This cannot be determined from the information given.
This statistical test examines the relationship between two sets of variables to determine whether they are associated or not. Group of answer choices ANOVA Pearson r Chi-square t-Test
State the null and alternative hypotheses for the situation described below for a statistical test. Testing to see if average sales are higher in stores where customers are approached
THE AAA reports that of the fatal car accidents, 54% are caused by driver error. If 3 accidents are chosen at random, find the probability that at least 1 is caused by driver error?
If the class mid points in a frequency distribution of age of a group of persons are 25, 32, 39, 46, 53 and 60. The size of class interval is: Question 37 options: A. 5 B. 7 C. 8 D. 6
Suppose that the two random variables X and Y have an exact linear relationship:Y= a bX where a and b are constants. What is the correlation coefficient (X,Y )between X and Y ?
A stoplight just turned red. The probability that a light turns green in the next x minutes is given by the  function f below where k is a constant.  f(x) =  kcos π 2x 1
Suppose that the true population mean is 52.1 and the true population standard deviation is 19.3. If you draw a sample of size 36 then the z value for a sample mean of 59.9 is what?
[STOP3A] Compare the 95% with the 99% confidence interval for the population mean, which is wider? Need to know the standard deviation. Need to know the standard error. 95% 99%
With case control studies, epidemiologists identify a group of subjects with particular outcomes and compare them to a group without the conditions. Group of answer choices True False
What is the probability that, for five girls and three boys standing in a line: a) All three boys are standing together. b) No two boys are standing next to each other
For a population with a standard deviation of σ = 5, what is the z-score corresponding to a score that is 15 points above the mean? Group of answer choices z = 3 z = 12 z = 5 z = 1
ompute the following probabilities: a) If and B, find or B. b) If P(A)=0.57,P(B)=0.35, and A and B are mutually exclusive, find or B. c) Let P(A)=0.4,P(B)=0.8. Assume that A
Blue Star Optical is conducting a satisfaction survey of its 10,000 customers. There will be 100 customers in the final sample. How would the company pull a systematic sample of 100?
The working lifetime, in years, of a particular model of client is normally distributed with mean 10 and variance 4. Calculate the 14th percentile of the working lifetime, in years.
Let X be a normal random variable with mean μ = 77.523 and standard deviation σ = 2.897, find the value x such that P (X > x) = 0.7967. Enter your answer in Akindi line 16
Chao is assessing the percentage of customers who have not returned to the Fruit-of-the-Month Club to estimate how many might leave on a yearly basis. What process is Chao working on?
In this exercise, test H0:p1=p2 vs Ha:p1>p2, with p1-p2 =0.8 -07 =0.10 for different sample sizes. In parts (a) and (b), use StatKey or other technology to find the p-value.
A researcher conducted a one way between subjects ANOVA and found a significant analysis result but decided to retain the null hypothesis. Should they report the effect size?
The amount of time, in minutes, that a person must wait for a bus is uniformly distrubuted between 0 and 23 minutes. What us the probability that a person waits more than 8 minutes
Consider the variable Sale Condition. It is Quantitative or Qualitative? Quantitative Qualitative Neither Quantitative nor Qualitative Not enough information to determine the answer
Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 X 90) is a. 0.5328. b. 0.3413. c. 0.1915. d. 0.1498.
The amount of time in minutes that a person must wait for a bus is uniformly distributed between 0 and 23 minutes. What is the probablity that a persoj waite more than 8 minutes.
If one sample has n = 10 scores with SS = 15 and a second sample has n = 10 scores with SS = 30, then the pooled variance will be _____. Group of answer choices 2.50 .75 2.25 1.50
What is the confidence level (written as a percentage) for the interval x̅-2.14 σ / √(n)≤μ≤x̅+2.14 σ / √(n) ? (Round your answer to 2 decimal places.) 8 Attempts: 0 of 1 used
Let X1 be a number selected randomly from the set {0, 10−3, 103} and let X2 be independent of X1 identically distributed. Let Y = X1X2. Compute E[X2|Y ̸ = 0].
Someone flips 15 biased coins once. The coins are weighted such that the probability of a head with any coin flip is .85 (P = .85). What is the probability of getting
Which of the following is a proper way to describe the probability of flipping heads on a fair coin? I. ½ II. 0.5 III. 50% a. I only b. III only c. I and III only d. I, II, and III
What is the confidence level (written as a percentage) for the interval x̅-2.49 σ / √(n)≤μ≤x̅+2.49 σ / √(n) ? (Round your answer to 2 decimal places.) 8 Attempts: 0 of 1 used
An assumption of ANOVA is that 1. all groups have the same variance 2. all groups are from Normal populations 3. all observations are independent 4. all of the above (1, 2, and 3)
For each of the following measures, give the value that implies no difference between the two groups being compared. (a) relative risk (b) odds ratio (c) percent increase in risk %
Can you use the confidence interval you constructed in part (a) to test the hypotheses H0 : µ = 11 versus Ha : µ ̸= 11 at 1% significance level? Briefly explain without a P-value.
A polling organization conducts a poll by making a random survey and is willing to accept a margin of error of 4% at a confidence level of 95%. What should the sample size be?
a judge is 63% sure that a suspect has committed a crime. during the course of a trial a witness convinces the judge that there is an 81% chance that the criminal is left handed
Consider a normal population distribution with the value of 𝜎 known. (a) What is the confidence level for the interval x ± 2.88𝜎⁄ n ? (Round your answer to one decimal place.)
If a coin is flipped 4 times, what is the probability of getting exactly 3 heads, given that at least 1 head is obtained? Question 5 options: 0.392 0.441 0.267 0.412 0.357
. A fair coin is tossed twice. Let X represent the number of heads obtained on the firsttoss and Y represent the total number of heads obtained in two tosses.
Market share turns out to be a strong, positive predictor of the company’s future customer satisfaction, because consumers prefer many choices in the market place. True or False?
If the probability then in the event will occur 1/3 and the probability that the event will not occur is 2/3 in the eyes in favor of the event occurring are simplify your answer
Suppose x has a normal distribution with mean 𝜇 = 29 and standard deviation 𝜎 = 4. Describe the distribution of x values for sample size n = 4. (Round 𝜎x to two decimal places.)
Two fair six-sided dice are rolled (one maize and one blue), with outcomes 𝑋 and 𝑌 respectively for the maize and the blue. (b) Are X + Y and X − Y independent? Explain.
A set of n = 4 scores has a mean of μ = 11. If 8 points are subtracted from one of the scores, what is the new value for the population mean? Group of answer choices 11 9 10 13
A study finds a correlation coefficient of r = .52. According to Cohen’s benchmarks, the magnitude of this effect is: a. multiply determined. b. categorical. c. large. d. modest.
Samples of size n = 9 are selected from a population with μ = 60 with σ = 20. What is the expected value for the distribution of sample means? Group of answer choices 60 80/3 6 18
Which is not an assumption for residuals in multiple regression? Group of answer choices Normally distributed Heteroskedasticity mean = 0 Variance is the same at all values of X
A normal population has a mean of $62 and standard deviation of $14. You select random samples of nine. What is the probability that a sample mean is between $58 and $65?
Suppose X and Y are random variables such that the standard deviation of X is 2 andthe standard deviation of Y is 5. Consider a random variable Z defined as:Z = 3X2Y 5
suppose that the life of a lightbulb, x, in thousands of hours is exponentially distributed random variable (one failure every 10,000 hours on average) compute p(X>12 | X>10)
What is the minimum sample size that would be needed to ensure that the length of the CI in part (a) is 0.5 µg/mL assuming the sample standard deviation remains at 2.0 µg/mL?
The obtained chi-square is 2512. Based on alpha of 0, what can you conclude about the relationship between gender and views on restoring the voting rights of felons in prison?
Determine if each event is independent or dependent. A green die and a red die are tossed. What is the probability that a 4 shows on the green die and a 5 shows on the red die?
If the moment-generating function of X is M(t) = exp(166t + 2007}), -00 < 1 < 00, find (a) The mean of X. (c) P(170 < X < 200). (b) The variance of X. (d) P(148 ≤ X ≤ 172).
A normal population has a mean of $61 and standard deviation of $13. You select random samples of nine. What is the probability that a sample mean is greater than $64?
If an analysis of variance is used for the following data, what would be the effect of changing the value of M1 to 20? Sample Data M1 = 15 , M2 = 10 SS1 = 90 , SS2 = 70
A normal population has a mean of $62 and standard deviation of $14. You select random samples of nine. What is the standard error of the sampling distribution of sample means?
Prove that for a two-variable regression model R 2 = r 2 where R is the coefficient of determination and r is the coefficient of correlation between X and Y.
The formula used to calculate a large-sample confidence interval for p is... What is the appropriate z critical value for each of the following confidence levels? 80% and 94%
A normal population has a mean of $60 and standard deviation of $12. You select random samples of nine. What is the standard error of the sampling distribution of sample means?
A normal distribution has a mean of u=70 and o=10. If one score is randomly selected from this distribution what is the probability that the score will be greater than x =82
A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. The probability that the sample mean is less than 15 is __________blank.
Which of the following sets of data has an interquartile range of 10 ? 12,14,17,19,19,20,21 55,56,56,57,58,59,62 41,43,49,49,50,53,55 3.4 .9 .16 .17 .24 .31
A researcher is conducted a study and finds degrees of freedom equal to (3,36). What will be the critical value of a one way between subjects ANKVA at .05 level of significance
A normal population has a mean of $60 and standard deviation of $12. You select random samples of nine. What is the probability that a sample mean is between $56 and $63?
A sample of n = 16 scores has a standard error of 4. What is the standard deviation of the population from which the sample was obtained? Group of answer choices 64 2 4 16
A study found that in blue collar jobs, with similar qualifications and general appearance, African Americans were offered jobs at about 50% the rate of Latinos. True or False
Would the margin of error for a 95% confidence interval increase or decrease if we increased the sample size to 600 (assume the value of is the same as part (c))? Why?(2 pts)
Wechsler classifies "visual-motor coordination" as a _______________________________. Group of answer choices Verbal Test Performance Test General Test Intelligence Test Next
A sample of 240 observations is selected from a normal population with a population standard deviation of 26. The sample mean is 15. Determine the standard error of the mean.
Tourists enter a museum at the rate of 0.4 tourists per second. There are, on average, 5,600 tourists in the museum. On average, how long does a tourist spend in the museum?
Would belief in the law of small numbers lead people to think that the two events in part (b) are equally likely, or are not equally likely? Would they be correct? Explain.
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