3. The average number of students at each university with gym memberships outside of their respective university's fitness center was1231 in 2017. In an effort to study whether this trend

is increasing in 2018and thus Boston's investment in a new student fitness center is unnecessary, Boston researchers took a simple random sample of 34universities. They found that the average number of students with external gym memberships from the 34 universities was 1233 with a standard deviation of 11. a. What are the null and alternative hypotheses? b. Calculate the test statistic C. Find the p-value d. What is your conclusion in context at the alpha significance level of .10? Did the number increase just by chance, or is there a reason to believe UConn made a mistake in their investment? e. If we know the population standard deviation is 13, how does this impact your test if conducted at the same alpha significance level of.10? If you need to run a different type of test, list your new hypotheses, the new test statistic, the new p-value, and the new conclusion.