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	74
Golfer 4	72	71
Golfer 5	70	69
Golfer 6	67	67
Golfer 7	71	67
Golfer 8	68	75
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	76
Golfer 15	68	70
Golfer 16	68	66
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) 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.)

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

Answer:

Given that,

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	74
Golfer 4	72	71
Golfer 5	70	69
Golfer 6	67	67
Golfer 7	71	67
Golfer 8	68	75
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	76
Golfer 15	68	70
Golfer 16	68	66
Golfer 17	71	70
Golfer 18	70	68
Golfer 19	69	68
Golfer 20	67	71

To test the hypothesis is that 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 10% level of significance.

The null and alternative hypothesis is:

(a).

The t-test statistics is,

By using MegaStat, find t-test statistics with the help of following steps is:

1). Import the data.

2). Select the MegaStat from Add-Ins option.

3). Select the Paired Observations groups from Hypothesis Tests.

4). Select data input.

5). Select confidence level. Test difference and alternative hypothesis.

6). Select t-test.

7). Click Ok.

Hypothesis Test: Paired Observations 0.000-hypothesized value 69.650-Mean first 70.550-Mean final -0.900- Mean difference (First-Final) 2.954- std. dev 0.661- std.error 20- n 19- df -1.363- t .1890- p-value (two tailed) -2.042- Confidence interval 90% lower 0.242 - Confidence interval 90% upper 1.142 -Margin of error

From the MegaStat output, the t-test statistics is -1.363.

The p-value for this test is,

From the MegaStat output, the p-value for this test is 0.1890.

Decision :

The conclusion is that the p-value in this context is higher than 0.10 which is 0.1890, so the null hypothesis is not rejected at 1% level of significance. There is insufficient evidence to indicate that the mean score for the first round of a golf tournament even is significantly different than the mean score for the fourth and final round. The result is not statistically significant.

(b).

The point estimate of the  difference between the two population means is,

For a MegaStat output in part (a), the point estimate of the difference between the two population means is -0.90.