Question

You may need to use the appropriate technology to answer this question.

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	75
Golfer 4	72	71
Golfer 5	70	69
Golfer 6	67	67
Golfer 7	71	67
Golfer 8	68	72
Golfer 9	67	71
Golfer 10	70	69

Player	First Round	Final Round
Golfer 11	72	72
Golfer 12	72	70
Golfer 13	70	73
Golfer 14	70	76
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 α = 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 μ_d = mean score first round − mean score fourth round.)

H₀: μ_d = 0

H_a: μ_d ≠ 0 CORRECT!!

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

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

p-value =

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

Answer 1

Ans.

Player	First Round(x)	Final Round(y)	d=x-y	d^2
Golfer 1	70	72	-2	4
Golfer 2	71	72	-1	1
Golfer 3	70	75	-5	25
Golfer 4	72	71	1	1
Golfer 5	70	69	1	1
Golfer 6	67	67	0	0
Golfer 7	71	67	4	16
Golfer 8	68	72	-4	16
Golfer 9	67	71	-4	16
Golfer 10	70	69	1	1
Golfer 11	72	72	0	0
Golfer 12	72	70	2	4
Golfer 13	70	73	-3	9
Golfer 14	70	76	-6	36
Golfer 15	68	70	-2	4
Golfer 16	68	65	3	9
Golfer 17	71	70	1	1
Golfer 18	70	68	2	4
Golfer 19	69	68	1	1
Golfer 20	67	71	-4	16
Sum =	1393	1408	-15	165