For the data of the previous exercise we want to compare population medians for the runs in Denver versus the runs in Phoenix.

Data From Previous Exercise

a. Use software to generate a bootstrap sample of differences of medians. Check the bootstrap distribution for normality using a normal probability plot.

b. Use the standard deviation of the bootstrap distribution along with the difference of the medians in the original sample and the t critical value from the previous exercise to get a 95% confidence interval for the difference of population medians.

c. Use the bootstrap sample and the percentile method to obtain a 95% confidence interval for the difference of population medians.

d. Compare the two confidence intervals.

e. How do the results for the median compare with the results for the mean? In terms of precision (measured by the width of the confidence interval) which gives the best results?

Transcribed Image Text:

In this application from major league base- ball, the populations represent an abstrac- tion of what the players can do, so the populations will vary from year to year. The Colorado Rockies and the Arizona Dia- mondbacks played nine games in Phoenix and ten games in Denver in 2001. The thinner air in Denver causes curve balls to curve less and it allows fly balls to travel farther. Does this mean that more runs are scored in Denver? The numbers of runs scored by the two teams in the nine Phoenix games (P) and ten Denver games (D) are P: D: 5.09 6.48 10 14 15.88 11.65 18 13.76 3 7.41 15.56 10 8.47 9.53 19 20.12 11.65 8.1 10.59 The fractions occur because the numbers have been adjusted for nine innings (54 outs). For example, in the third Denver game the Rockies won 10 to 7 on a home run with two out in the bottom of the tenth inning, so there were 59 outs instead of 54, and the number of runs is adjusted to (54/59)(17) = 15.56. We want to compare the average runs in Denver with the aver- age runs in Phoenix.