Question

A golf club manufacturer claims that golfers can lower their scores by using the manufacturer's newly designed golf clubs. Eight golfers are randomly selected and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are asked again to give their most recent score. The scores for each golfer are given in the table below. Is there enough evidence to support the manufacturer's claim?

Let d=(golf score after using the newly designed golf clubs)−(golf score before using the newly designed golf clubs). Use a significance level of α=0.05 for the test. Assume that the scores are normally distributed for the population of golfers both before and after using the newly designed clubs.

Golfer	1	2	3	4	5	6	7	8
Score (old design)	92	78	83	80	83	95	82	76
Score (new design)	87	82	80	75	90	91	77	72

Step 1 of 5 : State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test.

Answer 1

ANS.

Golfer	Score (Old)	Score (New)	d=New - Old	d-d_bar	(d-d_bar)^2
1	92	87	-5	-3.125	9.765625
2	78	82	4	5.875	34.515625
3	83	80	-3	-1.125	1.265625
4	80	75	-5	-3.125	9.765625
5	83	90	7	8.875	78.765625
6	95	91	-4	-2.125	4.515625
7	82	77	-5	-3.125	9.765625
8	76	72	-4	-2.125	4.515625
SUM =			-15		152.875
MEAN =			-1.875
Std. Dev. =			4.673

There is sufficient evidence that a golf club manufacturer claims that golfers can lower their scores by using the manufacturer's newly designed golf clubs was wrong.