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	73
Golfer 4	72	71
Golfer 5	70	69
Golfer 6	67	67
Golfer 7	71	68
Golfer 8	68	74
Golfer 9	67	73
Golfer 10	70	69

Player	First Round	Final Round
Golfer 11	72	72
Golfer 12	72	70
Golfer 13	70	73
Golfer 14	70	77
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

H₀:

μ_d ≠ 0

H_a:

μ_d = 0

     

H₀:

μ_d ≤ 0

H_a:

μ_d > 0

H₀:

μ_d > 0

H_a:

μ_d ≤ 0

H₀:

μ_d = 0

H_a:

μ_d ≠ 0

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 =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round.Do not reject H₀. There is insufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round.     Reject H₀. There is insufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round.Do not Reject H₀. There is sufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round.

(b)

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

For which round is the population mean score lower?

Answer 1

Ho :   µd=   0
Ha :   µd ╪   0

Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
70	72	-2.00	1.10
71	72	-1.00	0.00
70	73	-3.00	4.20
72	71	1.00	3.80
70	69	1.00	3.80
67	67	0.00	0.90
71	68	3.00	15.60
68	74	-6.00	25.50
67	73	-6.00	25.50
70	69	1.00	3.80
72	72	0.00	0.90
72	70	2.00	8.70
70	73	-3.00	4.20
70	77	-7.00	36.60
68	70	-2.00	1.10
68	65	3.00	15.60
71	70	1.00	3.80
70	68	2.00	8.70
69	68	1.00	3.80
67	71	-4.00	9.30

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	1393	1412	-19.000	176.950

mean of difference ,    D̅ =ΣDi / n =   -0.9500
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    3.0517

std error , SE = Sd / √n =    3.0517   / √   20   =   0.6824      
                          
t-statistic = (D̅ - µd)/SE = (   -0.95   -   0   ) /    0.6824   =   -1.392

------------

Degree of freedom, DF=   n - 1 =    19  
  
p-value =        0.1800 [excel function: =t.dist.2t(t-stat,df) ]

Conclusion:     p-value>α , Do not reject null hypothesis  

Do not reject H₀. There is insufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round.

b)

the point estimate of the difference between the two population means= -0.950
For first round is the population mean score lower