The manager of a minor league baseball team wants to estimate the average fastball speed of two pitchers. He clocks 50 fastballs, in miles per hour, for each pitcher. A portion of the data is shown in the accompanying table; the complete data set, labeled Fastballs, can be found on the text website.
Pitcher 1 Pitcher 2
87....... 82
86....... 92
: ........ :
86....... 93
a. Use Excel to construct 95% confidence intervals for the mean speed for each pitcher.
b. Explain why the widths of the two intervals are different.