When we considered the Boston Marathon in Exercise 37, we were unable to check the Nearly Normal Condition. Here's a histogram of the differences:

The three largest differences are the first three years of wheelchair competition: 1977, 1978, and 1979. Often the start-up 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 wheel chrF €“ run M n = 34
Mean = -13.40
SD = 20.57
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 ( = 0.05 reject the null hypothesis of no difference? What conclusion would you draw?

Transcribed Image Text:

20 15 10 -40 40 80 F Wheelchair-M Runners (minutes)