Question

Suppose that Adam is a candidate for city council in a large metropolitan area. While campaigning, he claimed that 65% 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 400 randomly selected adult city residents and found that 245 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 z-statistic were computed using the null hypothesis Ho:p = 0.65 where p is the proportion of all adults in the city who meet or exceed the CDC's recommendations for physical activity each week. Sample Sample Sample Standard z-Statistic size count proportion error SE 400 245 0.6125 0.0238 -1.5724 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 P-value of the z-statistic against the alternative hypothesis H1:p # 0.65 You may find this list of software manuals helpful. Give your answer in decimal form, with precision to four decimal places.

Answer 1

The statistical software output for this problem is :

P-value = 0.1159