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Chapter 9: Q T9.7. (page 616)

A95%confidence interval for the proportion of viewers of a certain reality television

show who are over 30 years old is (0.26,0.35). Suppose the show's producers want to est the hypothesis \H0:p=0.25against Ha: Ha:p≠0.25. Which of the following is an appropriate conclusion for them to draw at the α=0.05

a. Fail to reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals 0.25

b. Fail to reject H0there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

c. Reject H0; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

. d. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25.

e. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

Short Answer

Expert verified

RejectH0, there is convincing evidence that the true proportion of viewers differs from 0.25

Step by step solution

01

Step 1:Given information

A 95% confidence interval for the proportion of viewers of a certain reality television show who are over30 years old is(0.26,0.35).Suppose the show’s producers want to test the hypothesis H0: p=0.25 against Ha: p≠0.25.

02

Step 2:Explaination

It is observed that the confidence interval not having0.25,it is showing that it is not likely that the proportion of viewers of a certain actually television show is 0.25and therefore there is convincing proof that the proportion is different from 0.25(since the alternative hypothesis is H1:p≠0.25).

Hence, the correct option is (e)

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Most popular questions from this chapter

Interpreting a P-value A student performs a test of H0:μ=100H0:μ=100versus Ha: μ>100Ha:μ>100and gets a P-value of 0.044.The student says, "There is a0.044 probability of getting the sample result I did by chance alone." Explain why the student's explanation is wrong.

Error probabilities and power You read that a significance test at the α=0.01

significance level has probability 0.14of making a Type II error when a specific alternative is true.

a. What is the power of the test against this alternative?

b. What’s the probability of making a Type I error?

Better parking A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school’s students approved of the parking that was provided. After the change, the principal surveys an SRS of students at the school. She would like to perform a test of H0:p=0.37Ha:p>0.37where p is the true proportion of students at school who are satisfied with the parking

situation after the change.

a. The power of the test to detect that p=0.45 based on a random sample of 200 students and a significance level of α=0.05 is 0.75 Interpret this value.

b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).

c. Describe two ways to increase the power of the test in part (a).

Reality TVTelevision networks rely heavily on ratings of TV shows when deciding

whether to renew a show for another season. Suppose a network has decided that

“Miniature Golf with the Stars” will only be renewed if it can be established that more than 12%of U.S. adults watch the show. A polling company asks a random sample of 2000U.S. adults if they watch “Miniature Golf with the Stars.” The network uses the data to perform a test of

H0:p=0.12

Ha:p>0.12

where pis the true proportion of all U.S. adults who watch the show. Describe a Type Ierror and a TypeIIerror in this setting, and give a possible consequence of each.

Proposition XA political organization wants to determine if there is convincing evidence that a majority of registered voters in a large city favor Proposition X. In an SRS of 1000registered voters, 482favor the proposition. Explain why it isn’t necessary to carry out a significance test in this setting.
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