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Kacy Ledith

Kacy L.

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Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Before the overtime rule in the National Football League was changed in 2011 , among 460 overtime games, 252 were won by the team that won the coin toss at the beginning of overtime. Using a 0.05 significance level, test the claim that the coin toss is fair in the sense that neither team has an advantage by winning it. Does the coin toss appear to be fair?

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Before the overtime rule in the National Football League was changed in 2011 , among 460 overtime games, 252 were won by the team that won the coin toss at the beginning of overtime. Using a 0.05 significance level, test the claim that the coin toss is fair in the sense that neither team has an advantage by winning it. Does the coin toss appear to be fair?

Elementary Statistics

Hypothesis Testing

Testing a Claim About a Proportion
A study is done to see whether a coin is biased. The alternative hypothesis used is two-sided, and the obtained $z$ -value is 1 . Assuming that the sample size is sufficiently large and that the other conditions are also satisfied, use the Empirical Rule to approximate the p-value.

A study is done to see whether a coin is biased. The alternative hypothesis used is two-sided, and the obtained $z$ -value is 1 . Assuming that the sample size is sufficiently large and that the other conditions are also satisfied, use the Empirical Rule to approximate the p-value.

Essential Statistics: Exploring the World through Data

A test is conducted in which a coin is flipped 30 times to test whether the coin is unbiased. The null hypothesis is that the coin is fair. The alternative is that the coin is not fair. One of the accompanying figures represents the p-value after getting 16 heads out of 30 flips, and the other represents the p-value after getting 18 heads out of 30 flips. Which is which, and how do you know?

A test is conducted in which a coin is flipped 30 times to test whether the coin is unbiased. The null hypothesis is that the coin is fair. The alternative is that the coin is not fair. One of the accompanying figures represents the p-value after getting 16 heads out of 30 flips, and the other represents the p-value after getting 18 heads out of 30 flips. Which is which, and how do you know?

Essential Statistics: Exploring the World through Data

What is the relative magnitude of degree Rankine to degree Kelvin?

What is the relative magnitude of degree Rankine to degree Kelvin?

Fundamentals of Thermodynamics

Questions asked

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Ana Carolina Da Cruz verified

Numerade educator

The geometric distribution describes the total number of experiments k that one must perform before getting a success, assuming that each experiment is a Bernoulli trial with probability p. If X ∼ geom(p), then P(X = k) = (1 − p)k−1p 1. (2) Compute the likelihood in the parameter θ of a random sample X1, . . . , Xn of i.i.d geom(θ) random variables. 2. (2) Compute the log-likelihood for the previous sample. 3. (2) Compute the MLE. 4. (1) A company produces light-bulbs. They must estimate the probability that a light-bulb is faulty. They test random light-bulbs until they find one faulty and they record how many were tested before finding the faulty one. They repeat this process 5 times and record the following results 4, 32, 11, 22, 21 Estimate the probability θ that a light-bulb is faulty.

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David Nguyen verified

Numerade educator

PROBLEM 3 (6 points) X describes the throw of a fair sided dice. Y takes the value 1 if the dice comes up 6 or the value 0 otherwise. 1. (2) Write the joint distribution of X and Y , including the marginals. 2. (2) Compute the correlation between X and Y . 3. (2) Compute Var[X +Y]+Var[X −Y].

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ANSWERED

David Nguyen verified

Numerade educator

PROBLEM 2 (6 points) Let X be the random variable describing the age at the time of death of a fruit fly. We know that the median of X is about 6 days. 1. (2) Assume that X is uniformly distributed. What is its distribution? Compute the probabi- lity that a fruit fly lives up until 10 days. 2. (2) Assume instead that X is exponentially distributed. What is its distribution? Compute the probability that a fruit fly lives up until 10 days under these new model. 3. (2) If we know that in average a fruit fly lives about 8 days. Which of the previous 2 models would you choose for the life of a fruit fly?

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David Nguyen verified

Numerade educator

A diagnostic test for a disease is known to have a sensibility (i.e. the probability that the test is positive if the individual is infected) of 90% and specificity (i.e. the probability that the test comes up negative if the individual is healthy) of 70%. Half the tests in a massive screening yield positive results. 1. (3) Which is the frequency of the disease in the population? 2. (2) Which is the probability that an individual is infected if the test is positive

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Keondre Parker verified

Numerade educator

Exercise 4. Let X1, . . . , Xn, Xn+1 be a sample from a normal population having an unknown mean μ and variance 1. Let Xn = 1/n ∑i=1 to n Xi be the average of the first n of them. i) What is the distribution of Xn+1 − Xn? (ii) If Xn = 4, give an interval that, with 95% confidence, will contain the value of Xn+1.

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Robin Corrigan verified

Numerade educator

Exercise 6. A random sample of 100 items from a production line revealed 17 of them to be defective. Compute an approximate 95% percent two-sided confidence interval for the probability that an item produced is defective. What assumptions do you use? Notice that this is not a Gaussian sample

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T. L. verified

Numerade educator

Exercise 5. Suppose that a random sample of nine recently sold houses in a certain city resulted in a sample mean price of $222, 000, with a sample standard deviation of $22,000. Give a 95% upper confidence interval for the mean price of all recently sold houses in this city.

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ANSWERED

T. L. verified

Numerade educator

Exercise 3. An electric scale gives a reading equal to the true weight plus a random error that is normally distributed with mean 0 and standard deviation σ = .1 mg. Suppose that the results of five successive weighings of the same object are as follows: 3.142,3.163,3.155,3.150,3.141. Determine a 95% confidence intervaL

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David Nguyen verified

Numerade educator

Exercise 2. Let X1, . . . , Xn be a sample from the distribution whose density function is f(x) = 12e−|x−θ|, x ∈ R. Determine the maximum likelihood estimator of θ. [Hint: the usual method of differentiating does not work. Once you find the log-likelihood, you must carefully minimize the sum that appears there.

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ANSWERED

David Nguyen verified

Numerade educator

Exercise 1. Let X1, . . . , Xn be a sample from the distribution whose density function is f(x) = e−(x−θ), x ≥ θ; 0 otherwise Determine the maximum likelihood estimator of θ. [Hint: one must reason similarly as to the uniform distribution]

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