Your classmates were invited to answer a MATH 1P98 student survey. You will work with the results from that survey. Students were asked, "How many days in a week do you exercise for more than 20 minutes?". Students could choose to respond between 0 days to 7 days. See the Excel sheet for results.

Part A:

A fitness trainer is interested in finding out the true mean number of days that MATH 1P98 students exercise in a week. The trainer claims that the mean number of days in a week that

MATH 1P98 students exercise for more than 20 minutes is 3.5 days. Test this claim

at the 0.05 level of significance.

a. State the null and alternative hypotheses. Indicate the significance level.

b. Identify the test statistic you will use. Are the requirements needed to use that

test statistic satisfied? Explain. (Hint: How do you decide between using ? or jQuery22401237312698696873_1606263744802

Check if the data follows a normal distribution and/or sample size.)

c. Use Excel to obtain any sample statistics necessary to calculate the test statistic.

(show Excel sheet.) Then, calculate the test statistic by hand.

e. Write the critical value(s) used for this test. Compare your test statistic to explain

whether or not the null hypothesis is rejected.

f. Write concluding statement that addresses the fitness trainer's claim.

Part B:

A fitness trainer is interested in finding out if there is a difference between the mean number of days that female MATH 1P98 students exercise and the mean number of days that male 4 MATH 1P98 students exercise. When completing the survey, respondents could self-identify their gender. Students without a response in the Gender column either preferred not to answer or self-identified differently from "female" or "male". Because the focus of this study is interested in comparing exercise days between female and male students, we will only consider the exercise data available for the 1 = 185 students who identified as female and the 2 = 236 students who identified as male.

a. Use Excel to compute the summary statistics for each sample. Since you will use these values in calculations, write and with four decimals. For this part, submit only the completed table. Female Male

b. Identify whether the two samples are independent or dependent. Provide an explanation.

d. Use the sample data to construct a 95% confidence interval by hand to estimate the mean difference of the exercise days between female students and male students. Show your work, including all calculations.

e. Report the 95% confidence interval with three decimal places. Interpret this confidence interval in the context of the problem.

g. Does the confidence interval suggest there is a difference between the number of days that female MATH 1P98 students exercise and the number of days that male MATH 1P98 students exercise? Explain how you know. If there is a difference, identify which group exercises on more days, on average.

Link to survey results: https://drive.google.com/file/d/1pS0RpiL_8NvCcGtpnN4Knm0vx-IxFqZy/view?usp=sharing

Please label answers as part A (a), Part A(b), Part A(c), ... etc