AnswersAQR_A_ICTesting a Claim about a Difference between Proportions

Testing a Claim about a Difference between Proportions Answers

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An exercise scientist claims that exercise is the closest thing we have to a miracle drug, especially when it comes to sleeping well. The scientist claims that 92% of adult runners sleep well at night. To investigate this claim, an independent study selects a random sample of 200 adult runners and finds that 95% of them sleep well at night. Do these data provide convincing evidence that the true proportion of all adult runners who sleep well at night is different than 92%? The z-table can be found here.What is the correct test statistic, P-value, and conclusion of this test?

A
z = –1.56, P-value = 0.118, reject H0. We have convincing evidence to conclude that the true proportion of all adult runners who sleep well at night is different than 92%.
B
z = 1.56, P-value = 0.059, reject H0. We have convincing evidence to conclude that the true proportion of all adult runners who sleep well at night is different than 92%.
C
z = 1.56, P-value = 0.118, fail to reject H0. We do not have convincing evidence to conclude that the true proportion of all adult runners who sleep well at night is different than 92%.
D
z = 0.95, P-value = 0.059, fail to reject H0. We do not have convincing evidence to conclude that the true proportion of all adult runners who sleep well at night is different than 92%.

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