Arnold Palmer and Tiger Woods are two of the best golfers ever to play the game. To show how these two golfers would compare if both were playing at the top of their game, the following data provides the results of 18-hole scores during PGA competition. Palmer's scores are from his 1960 season, while Woods' scores are from his 1999 season.
Arnold Palmer Tiger Woods
n_{1}= 112 n_{2}= 84
_{x‾1}= 69.95 x‾_{2} = 69.56
Assume that the population standard deviation was 2.5 strokes for both golfers. Test the hypothesis that there was no difference between the scores of the two golfers at the 1% significance level. Show all steps.