When we considered the Boston Marathon in Exercise 43, we were unable to check the Nearly Normal Condition. Here’s a histogram of the differences:

Those three large differences are the first three years of wheelchair competition: 1977, 1978, and 1979. Often the startup years of new events are different; later on more athletes train and compete. If we omit those three years, the summary statistics change as follows:

Summary of wheelchair F - run M
n = 28
Mean = 12.1780
SD = 19.5116

a) Comment on the assumptions and conditions.

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

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

Transcribed Image Text:

15 10 -50 50 100 wheelchair F-run M Number of Marathons 5.