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

          n₁=                 112                                  n₂=    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.