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) 93 86 84 96 89 81 92 94

Score (new design) 91 90 80 92 91 77 89 87

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: Find the p-value for the hypothesis test. Round your answer to four decimal places.

Step 5 of 5: Draw a conclusion for the hypothesis test.

Answer 1

Step 1 of 5:

H0: Null Hypothesis: 0

HA: Alternative Hypothesis: < 0

Step 2 of 5:
New (X)            Old (Y)          d = X - Y

91                     93                 - 2

90                     86                 4

80                    84                   - 4

92                   96                 - 4

91                    89                 2

77                     81              - 4

89                    92                - 3

87                    94              - 7

From d values, the following statistics are calculated:

n = 8

= - 18/8 = - 2.25

s_d = 3.5757

So,

Standard deviation of the paired differences = 3.6.

Step 3 of 5:
SE = s_d/

= 3.5757/ = 1.2642

Test statistic is:

t =/SE

= - 2.25/1.2642 = - 1.7798

So,

test statistic is = - 1.780

Step 4 of 5:

ndf = n - 1 = 8 - 1 = 7

One Tail - Left side test

By Technology, p-value = 0.0592

So,

p-value = 0.0592

Step 5 of 5:

Since p-value is greater than = 0.05, Fail to reject H0.

Conclusion:

The data do not support the claim that golfer can lower their score by using the manufacturer's newly designed golf clubs.