Question

Scores in the first and final rounds for a sample of 20 golfers who competed in tournaments are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

	A	B	C	D
1	Player	First Round	Final Round	Differences
2	Michael Letzig	74	76	-2
3	Scott Verplank	76	66	10
4	D.A. Points	74	67	7
5	Jerry Kelly	71	72	-1
6	Soren Hansen	66	74	-8
7	D.J. Trahan	76	74	2
8	Bubba Watson	69	73	-4
9	Reteif Goosen	77	66	11
10	Jeff Klauk	69	65	4
11	Kenny Perry	68	73	-5
12	Aron Price	71	77	-6
13	Charles Howell	71	75	-4
14	Jason Dufner	65	75	-10
15	Mike Weir	68	65	3
16	Carl Pettersson	74	67	7
17	Bo Van Pelt	73	72	1
18	Ernie Els	69	77	-8
19	Cameron Beckman	76	68	8
20	Nick Watney	65	70	-5
21	Tommy Armour III	77	73	4

Suppose you would like to determine if the mean score for the first round of an event is significantly different than the mean score for the 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 a = .10 to test for a statistically significantly difference between the population means for first- and final-round scores. What is the p-value?

p-value is .8904 (to 4 decimals)

What is your conclusion?

There is no significant difference between the mean scores for the first and final rounds.

b. What is the point estimate of the difference between the two population means?

.20 (to 2 decimals)

For which round is the population mean score lower?

Final round

c. What is the margin of error for a 90% confidence interval estimate for the difference between the population means?

?????? (to two decimals)

Could this confidence interval have been used to test the hypothesis in part (a)?

Yes

Explain.

Use the point of the difference between the two population means and add and subtract this margin of error. If zero is in the interval the difference is not statistically significant. If zero is not in the interval the difference is statistically significant.

Answer 1

	Before	After	Difference (di)	di-dbar
	74	76	-2	4.84
	76	66	10	96.04
	74	67	7	46.24
	71	72	-1	1.44
	66	74	-8	67.24
	76	74	2	3.24
	69	73	-4	17.64
	77	66	11	116.64
	69	65	4	14.44
	68	73	-5	27.04
	71	77	-6	38.44
	71	75	-4	17.64
	65	75	-10	104.04
	68	65	3	7.84
	74	67	7	46.24
	73	72	1	0.64
	69	77	-8	67.24
	76	68	8	60.84
	65	70	-5	27.04
	77	73	4	14.44
Total	1429	1425	4	779.44

To Test :-

H₀ :-

H₁ :-  

Part a. Use a = .10 to test for a statistically significantly difference between the population means for first- and final-round scores. What is the p-value?

Test Statistic :-

P value = P ( X < 0.140) looking in t table for value 0.140 across ( n-1) degree of freedom

n-1 = 20 - 1 = 19

We can see 0.140 lies between 0.000 & 0.688 across 19 degree of freedom

0.000 has P value 1.00 & 0.688 has P value 0.50

0.50 < P value < 1.00

Using excel we found the exact P value for 0.140 is 0.8904

Test Criteria :- Rejet null hypothesis if P value < level of significance

0.8904 > 0.10, hence we fail to reject null hypothesis

Conclusion :- Accept Null hypothesis

b. What is the point estimate of the difference between the two population means?

Point estimate between population means is

Point Estimate   = 71.45 - 71.25 = 0.2

For which round is the population mean score lower?

, hence final round score lower.

c. What is the margin of error for a 90% confidence interval estimate for the difference between the population means?

Confidence Interval

( from statistical t table across 19 degree of freedom at )

Lower Limit =  

Upper Limit =

Margin of Error is