Question

Suppose that Adam is a candidate for city council in a large metropolitan area. While campaigning, he claimed that 61% of adult city residents meet or exceed the recommendations of the Center for Disease Control and Prevention (CDC) for physical activity each week. Jim, a reporter for a local fact-checking website, suspects that Adam pulls numbers out of thin air without doing any research. To test Adam's assertion, Jim surveyed 320 randomly selected adult city residents and found that 181 of them meet or exceed the CDC's recommendations for weekly physical activity. Jim's sample statistics are summarized in the table. The standard error and ? ‑statistic were computed using the null hypothesis ?0:?=0.61 where ? is the proportion of all adults in the city who meet or exceed the CDC's recommendations for physical activity each week. Sample size Sample count Sample proportion Standard error ?- Statistic ? ? ?̂ ?? ? 320 181 0.5656 0.0273 −1.6275 Do the data summarized in the table provide evidence that Adam's claim was incorrect? To help answer this question, use software to determine the ?-value of the ?- statistic against the alternative hypothesis ?1:?≠0.61 You may find this list of software manuals helpful. Give your answer in decimal form, with precision to four decimal places.

Answer 1

Given that, the null and alternative hypotheses are,

H0 : p = 0.61

H1 : p ≠ 0.61

n = 320 and x = 181

=> sample proportion = 181/320 = 0.565625

standard error (SE) is,

Test statistic is,

=> Z = -1.6275

Using Excel we find the p-value as follows :

Excel Command : =2 * NORMSDIST (-1.6275) = 0.1036

=> p-value = 0.1036