All work must be shown step by step. When using Excel for calculations list the Excel functions used and when they were used and explain how you arrived at the answers. Attach the Excel file.

Player Round 1 Round 2

1. Michael Letzig 70 72
2. Scott Verplank 71 72
3. D.A. Points 70 75
4. Jerry Kelly 72 71
5. Soren Hansen 70 69
6. D.J. Trahan 67 67
7. Bubba Watson 71 67
8. Reteif Goosen 68 75
9. Jeff Klauk 67 73
10. Kenny Perry 70 69
11. Aron Price 72 72
12. Charles Howell 72 70
13. Jason Dufner 70 73
14. Mike Weir 70 77
15. Carl Pettersson 68 70
16. Bo Van Pelt 68 65
17. Ernie Els 71 70
18. Cameron Beckman 70 68
19. Nick Watney 69 68
20. Tommy Armour III 67 71

Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in the PGA tournaments are listed above. 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. You are curious: 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?

1.Use to test for a statistically significant difference between the populations means for the first- and fourth-round scores. What is the p-value? What is your conclusion?

2.What is the point estimate for the difference between the two population means? For which round is the population mean score lower?

3.Develop a 90% confidence interval estimate for the difference between the population means. Use the single population methodology where the confidence interval is given by . Notice that 0 is in this interval: what does this say about the statistical significance of the difference in the means?