An independent golf equipment testing facility compared the difference in the performance of golf balls hit off a regular 2-3/4'' wooden tee to those hit off a 3'' Stinger Competition golf tee. A Callaway Great Big Bertha driver with 10 degrees of loft was used for the test, and a robot swung the club head at approximately 95 miles per hour. Data on total distance traveled (in yards) with each type of tee, based on the test results, are provided on the WeissStats CD.
a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples.
b. At the 1% significance level, do the data provide sufficient evidence to conclude that, on average, the Stinger tee improves total distance traveled?
c. Find a 99% confidence interval for the difference between the mean total distance traveled with the regular and Stinger tees.
d. Are your procedures in parts (b) and (c) justified? Why or why not?