Question

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 freshmen intramural participants have higher freshman-year GPA's than freshmen who do not participate in intramurals. Let μ_P be the mean freshmen year GPA of intramural participants and μ_N be the mean freshmen year GPA of intramural nonparticipants. Do these data support the claim that freshmen intramural participants have higher freshmen year mean GPA's than freshmen intramural nonparticipants? Perform the appropriate hypothesis test and answer the questions below (calculate the difference as participant freshmen year GPA - nonparticipant freshmen year GPA.

excel file- https://docs.google.com/spreadsheets/d/e/2PACX-1vS5eS0C7pu0kxQEOPYnJnrWThBOxuYztqXcdjp6xPL06Elf8r4OhwLsjPNk1xdads9Le3Xb2qsZroML/pubhtml?gid=0&single=true

copy the file into a browser

Question 1. What is the value of the test statistic t? (use 2 decimal places in your answer)

Question 2. Select the correct choice below for the P-value of this hypothesis test.

-0.005 < P-value < 0.01

-P-value > 0.10    

-0.05 < P-value < 0.10

-0.01 < P-value < 0.05

-0.001 < P-value < 0.005

-P-value < 0.0001

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

-There is insufficient evidence to conclude that the mean freshmen year GPA of intramural participants is greater than the mean freshmen year GPA of intramural nonparticipant.

-There is sufficient evidence to conclude that the mean freshmen year GPA of intramural participants is greater than the mean freshmen year GPA of intramural nonparticipants.

-There is sufficient evidence to conclude that the mean freshmen year GPA of intramural participants is less than the mean freshmen year GPA of intramural nonparticipants.

Question 4. Estimate the mean difference (freshmen year intramural participant GPA - freshmen year intramural nonparticipant GPA) in freshmen year GPA's with a 95% confidence interval.

- lower bound of interval (use 4 decimal places)

- upper bound of interval (use 4 decimal places)

Answer 1

A claim frequently made by college academic advisors is that freshmen intramural participants have higher freshman-year GPA's than freshmen who do not participate in intramurals. Let μP be the mean freshmen year GPA of intramural participants and μN be the mean freshmen year GPA of intramural nonparticipants. Do these data support the claim that freshmen intramural participants have higher freshmen year mean GPA's than freshmen intramural nonparticipants? Perform the appropriate hypothesis test and answer the questions below (calculate the difference as participant freshmen year GPA - nonparticipant freshmen year GPA.

Step to find the hypothesis to conduct in excel.

Step 1 : Put the data in excel as shown.

Step 2 : Go to Data -> Data Analysis -> ttest two sample assuming equal variance.

STep 3 : Input the values are shown.

Step 4 : The output is generate,we use the highlighted part as we using a one tail test.

Hypothesis :
Ho: The difference between mean GPA of freshmen intramural participants and freshmen intramural nonparticipants is equal.

H1: The difference between mean GPA of freshmen intramural participants and freshmen intramural nonparticipants is greater than zero.

We see the pvalue of the test (pvalue = 0.0000) is less than 0.05, hence we reject the null hypothesis.

We conclude that there is sufficient to support the claim that freshmen intramural participants have higher freshmen year mean GPA's than freshmen intramural nonparticipants

Question 1. What is the value of the test statistic t? (use 2 decimal places in your answer)
4.89

Question 2. Select the correct choice below for the P-value of this hypothesis test.
-P-value < 0.0001

Question 3. What is an appropriate conclusion for this hypothesis test?

-There is sufficient evidence to conclude that the mean freshmen year GPA of intramural participants is greater than the mean freshmen year GPA of intramural nonparticipants.

Question 4. Estimate the mean difference (freshmen year intramural participant GPA - freshmen year intramural nonparticipant GPA) in freshmen year GPA's with a 95% confidence interval.

confidence interval is (0.0963, 0.2253)

THe hypothesis is done by hand.

95% confidence interval calculation.