Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in golf tournaments are shown in the following table.

Player First Round Final Round

Golfer 1 70 72

Golfer 2 71 72

Golfer 3 70 73

Golfer 4 72 71

Golfer 5 70 69

Golfer 6 67 67

Golfer 7 71 68

Golfer 8 68 73

Golfer 9 67 72

Golfer 10 70 69

Player First Round Final Round

Golfer 11 72 72

Golfer 12 72 70

Golfer 13 70 73

Golfer 14 70 75

Golfer 15 68 70

Golfer 16 68 65

Golfer 17 71 70

Golfer 18 70 68

Golfer 19 69 68

Golfer 20 67 71

Suppose you would like to determine if the mean score for the first round of a golf tournament 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?

(a) Use= 0.10 to test for a statistically significantly difference between the population means for first- and fourth-round scores.

State the null and alternative hypotheses. (Use_d= mean score first roundmean score fourth round.)

H₀:

_d= 0

H_a:

_d0

Calculate the value of the test statistic. (Round your answer to three decimal places.)

Calculate thep-value. (Round your answer to four decimal places.)

(b) What is the point estimate of the difference between the two population means? (Usemean score first roundmean score fourth round.)

(c) What is the margin of error for a 90% confidence interval estimate for the difference between the population means? (Round your answer to two decimal places.)