The Boston Marathon has had a wheelchair division since 1977. Who do you think is typically faster, the men’s marathon winner on foot or the women’s wheelchair marathon winner? Because the conditions differ from year to year, and speeds have improved over the years, it seems best to treat these as paired measurements. Here are summary statistics for the pairwise differences in finishing time (in minutes):

Summary of wheelchrF - runM
N = 40
Mean = -7.27
SD = 33.568

a) Comment on the assumptions and conditions.

b) Assuming that these times are representative of such races and the differences appeared acceptable for inference, construct and interpret a 95% confidence interval for the mean difference in finishing times.

c) Would a hypothesis test at α = 0.05 reject the null hypothesis of no difference? What conclusion would you draw?

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