Chapter 10.3, Problem 26E

Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in PGA tournaments are shown in the following table. Suppose you would like to determine if the mean score for the first round of a PGA Tour event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down?

Player	First Round	Final Round
Michael Letzig	70	72
Scott Verplank	71	72
D. A. Points	70	75
Jerry Kelly	72	71
Soren Hansen	70	69
D. J. Trahan	67	67
Bubba Watson	71	67
Reteif Goosen	68	75
Jeff Klauk	67	73
Kenny Perry	70	69
Aron Price	72	72
Charles Howell	72	70
Jason Dufner	70	73
Mike Weir	70	77
Carl Pettersson	68	70
Bo Van Pelt	68	65
Ernie Els	71	70
Cameron Beckman	70	68
Nick Watney	69	68
Tommy Armour III	67	71

1. a. Use α = .10 to test for a statistically significantly difference between the population means for first- and fourth-round scores. What is the p-value? What is your conclusion?
2. b. What is the point estimate of the difference between the two population means? For which round is the population mean score lower?
3. c. What is the margin of error for a 90% confidence interval estimate for the difference between the population means? Could this confidence interval have been used to test the hypothesis in part (a)? Explain.