Introductory statistics students fill out a survey on the first day of class. One of the questions asked is €˜€˜How many hours of exercise do you typically get each week?€ Responses for a sample of 50 students are introduced in Example 3.25 on page 207 and stored in the file Exercise Hours. The summary statistics are shown in the computer output. The mean hours of exercise for the combined sample of 50 students is 10.6 hours per week and the standard deviation is 8.04. We are interested in whether these sample data provide evidence that the mean number of hours of exercise per week is different between male and female statistics students.  

Discuss whether or not the methods described below would be appropriate ways to generate randomization samples that are consistent with H₀: μ_F = μ_M vs H_a: μ_F ‰  μ_M. Explain your reasoning in each case.

(a) Randomly label 30 of the actual exercise values with €˜€˜F€ for the female group and the remaining 20 exercise values with €˜€˜M€ for the males. Compute the difference in the sample means, xÌ…_F ˆ’ xÌ…_M.

(b) Add 1.2 to every female exercise value to give a new mean of 10.6 and subtract 1.8 from each male exercise value to move their mean to 10.6 (and match the females). Sample 30 values (with replacement) from the shifted female values and 20 values (with replacement) from the shifted male values. Compute the difference in the sample means, xÌ…_F €“ xÌ…_M.

(c) Combine all 50 sample values into one set of data having a mean amount of 10.6 hours. Select 30 values (with replacement) to represent a sample of female exercise hours and 20 values (also with replacement) for a sample of male exercise values. Compute the difference in the sample means, xÌ…_F ˆ’ xÌ…_M.

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Variable Gender N Mean StDev Minimum Maximum 7.41 F 30 M 20 12.40 Exercise 9.40 0.00 34.00 8.80 2.00 30.00