Student affairs departments at colleges provide programs and events that offer students opportunities to learn outside of traditional coursework. one popular avenue of engagement chosen by students is intramural sports. does participation in intramural sports improve freshmen academic indicators such as gpa and retention after the first year?

this excel file freshmen intramurals has data on 745 intramural participant/nonparticipant pairs of freshmen at a large midwestern university. the student participant/nonparticipant pairs were formed based on matching gender and high school gpa (to within 0.25).

a claim frequently made by college academic advisors is that more than 73% of freshmen intramural participants do well enough academically to be retained to the next school year (that is, they do not flunk out). to evaluate this claim use the data in the excel file to perform the hypothesis test

h0: p = 0.73
ha: p > 0.73

where p is the population proportion of all freshmen intramural participants that are retained to the next school year.

question 1. what is the value of the test statistic z? (use 2 decimal places in your answer)

question 2. what is the p-value? (use 3 decimal places in your answer)

question 3. what is an appropriate conclusion for this hypothesis test? (1 submission allowed)

do not reject h0: p = 0.73; there is insufficient evidence to conclude that the population proportion p of freshmen intramural participants differs from 0.73.

reject h0: p = 0.73; there is sufficient evidence to conclude that p is greater than 0.73.

reject h0: p = 0.73; there is sufficient evidence to conclude that p is less than 0.73.

question 4. calculate a 98% confidence interval for the proportion p of all intramural participants that are retained to the next school year.(round to 4 decimal places).