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)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=0.05α=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)	8787	7575	9191	8585	8787	8080	8282	8787
Score (new design)	8585	7979	8888	7979	9090	7676	7878	8181

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

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

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

Step 4:Determine the decision rule for rejecting the null hypothesis H 0 H 0. Round the numerical portion of your answer to three decimal places.

Step 5: accept or reject null?

Answer 1

The statistical software output for this problem is:

From above output:

Step - 1: Hypotheses:

H₀ : μ_D> 0
H_A : μ_D < 0

Step - 2: Standard deviation = 3.8

Step - 3: Test statistic = -1.671

Step - 4: Reject Ho if t < -1.895

Step - 5: Fail to Reject Null Hypothesis