Arnold Palmer and Tiger Woods are two of the best golfers to ever play the game. The question was raised as to how these two golfers would have compared if both were playing at the top of their game. The following sample data show the results of 18-hole scores during  a PGA tournament competition. Palmer's scores are from his 1960 season, while Wood's scores are from his 1999 season (Golf Magazine, February 2000).

Use the sample results to test the hypothesis of no difference between the population mean 18-hole scores for the two golfers.  (The mean value represents the numerical mean of the scores taken from the rounds of golf played, represented by N)

                  Palmer, 1960                                    Woods, 1999
                  Mean = 69.95                                    Mean = 69.56
                  N = 112                                              N = 84

a. Assuming a population standard deviation of 2.5 for both golfers, what is the value of the test statistic?
b. What is the p-value?
c. Using alpha = .01, what is your conclusion?

Write up your results, show the null and alternate hypotheses, set up the problem and show the test statistic.