Question

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Player	Round 1	Round 2
Michael Letzig	70	72
Scott Verplank	71	72
D.A. Points	70	75
Jerry Kelly	72	71
Soren Hansen	70	69
D.J. Trahan	67	67
Bubba Watson	71	67
Reteif Goosen	68	75
Jeff Klauk	67	73
Kenny Perry	70	69
Aron Price	72	72
Charles Howell	72	70
Jason Dufner	70	73
Mike Weir	70	77
Carl Pettersson	68	70
Bo Van Pelt	68	65
Ernie Els	71	70
Cameron Beckman	70	68
Nick Watney	69	68
Tommy Armour III	67	71

Chapter 10 (Excel file included):

Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in the PGA tournaments are included in the attached Excel file. 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?

Answer 1

H₀: or the mean score for the first round of a PGA Tour event is not significantly different than the mean score for the fourth and final round

H₁: or 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.

1.We enter the values is excel as follows:

Player	Round 1	Round 2
Michael Letzig	70	72
Scott Verplank	71	72
D.A. Points	70	75
Jerry Kelly	72	71
Soren Hansen	70	69
D.J. Trahan	67	67
Bubba Watson	71	67
Reteif Goosen	68	75
Jeff Klauk	67	73
Kenny Perry	70	69
Aron Price	72	72
Charles Howell	72	70
Jason Dufner	70	73
Mike Weir	70	77
Carl Pettersson	68	70
Bo Van Pelt	68	65
Ernie Els	71	70
Cameron Beckman	70	68
Nick Watney	69	68
Tommy Armour III	67	71

2.Then click on data--->dataanalysis---->t-test:two samples assuming equal variances.

The output is as follows for two tailed test:

t-Test: Two-Sample Assuming Equal Variances
	Variable 1	Variable 2
Mean	69.65	70.7
Variance	2.765789474	9.168421053
Observations	20	20
Pooled Variance	5.967105263
Hypothesized Mean Difference	0
df	38
t Stat	-1.359275376
P(T<=t) two-tail	0.182071918
t Critical two-tail	2.024394164

since, |t|=1.35927<tc=2.024394 we accept the null hypothesis hence,the mean score for the first round of a PGA Tour event is not significantly different than the mean score for the fourth and final round

2.p-value=0.1820719>0.05 hence we accept the null hypothesis.

3.A point estimate for the difference in two population means is simply the difference in the corresponding sample means.

hence,point estimate for difference of means=70.7-69.65=1.05

4.

90% confidence interval:

Player	Round 1	Round 2	Difference
Michael Letzig	70	72	-2
Scott Verplank	71	72	-1
D.A. Points	70	75	-5
Jerry Kelly	72	71	1
Soren Hansen	70	69	1
D.J. Trahan	67	67	0
Bubba Watson	71	67	4
Reteif Goosen	68	75	-7
Jeff Klauk	67	73	-6
Kenny Perry	70	69	1
Aron Price	72	72	0
Charles Howell	72	70	2
Jason Dufner	70	73	-3
Mike Weir	70	77	-7
Carl Pettersson	68	70	-2
Bo Van Pelt	68	65	3
Ernie Els	71	70	1
Cameron Beckman	70	68	2
Nick Watney	69	68	1
Tommy Armour III	67	71	-4

for mean---->AVERAGE() function is used.

Mean=

-1.05

for sample sd----->STDEV.S() function is used.

Sample sd=

3.316228041

for Margin of error---->CONFIDENCE.T() function is used.

Margin of error(E)=

1.282205813

lower limit=mean-E and upper limit=mean+E at 90% confidence interval:

Lower limit(mean-E)	-2.33220581
Upper limit(mean+E)	0.232205813

please rate my answer and comment for doubts.