Question: A 9 hole golf course was supposed to have a par of 30, but over a long period, the population of golfers who played this course had a mean of m = 38.2 with σ = 3.3.

A designer was called to extend his course to 18 holes, on the understanding that the last nine would have the same difficulty level as the first nine. After the course was finished a random sample of 121 golfers played the course and produced an average score of 42.6 on the last nine holes. Given this sample was drawn from the population who played the old 9 holes, test the hypothesis that the 2 sets of 9 holes are truly equal in difficulty. Use an α value of .05. Construct the 95% confidence interval around \(\bar{X}\)