Question

A golf club manufacturer claims that golfers can lower their scores by using the manufacturer’s newly designed golf clubs. Eight (8) golfers are randomly selected, and each is asked to give his or her most recent score. The scores for each golfer are shown in the table below:

Golfer	Score (old design)	Score (new design)
1	89	83
2	84	83
3	96	92
4	82	84
5	74	76
6	92	91
7	85	80
8	91	91

Assuming the golf scores are normally distributed, at alpha = 0.10, determine whether there is enough evidence to support the manufacturer’s claim by specifically following and addressing the questions below:

2. Identify the claim and state the null and alternative hypotheses, Ho and Ha
3. Specify the level of significance, alpha, and the degree of freedom, d.f.
4. Find the critical values and identify the rejection region
5. Calculate the mean of the difference between pair data entries in the dependent sample, and the standard deviation of the between pair data entries in the dependent sample
6. Use the t-test to Use the t-test to find the standardized test statistic t
7. Determine whether to reject or fail to reject the null hypothesis
8. Interpret your decision in the context of the original claim

Answer 1

Golfer	Score (old design)	Score (new design)	Difference = d=old - new
1	89	83	6	36
2	84	83	1	1
3	96	92	4	16
4	82	84	-2	4
5	74	76	-2	4
6	92	91	1	1
7	85	80	5	25
8	91	91	0	0
Total			13	87

1.Identify the claim and state the null and alternative hypotheses, Ho and Ha

The claim states that golfers can lower their scores by using the manufacturer’s newly designed golf clubs.

d= scores (old design) - scores (new design)

state the null and alternative hypotheses, Ho and Ha:

2. Specify the level of significance, alpha, and the degree of freedom, d.f.

Assuming the golf scores are normally distributed, at alpha = 0.10

3. Find the critical values and identify the rejection region

the critical values =

4. Calculate the mean of the difference between pair data entries in the dependent sample, and the standard deviation of the between pair data entries in the dependent sample

5. Use the t-test to find the standardized test statistic t

Under Ho:

Our test statistic is given by

6. Determine whether to reject or fail to reject the null hypothesis

Since our calculates t value falls in the rejection region i.e. t(cal ) > t(tabulated) value we have sufficient evidence to reject Ho at 10% level of significance.

7. Interpret your decision in the context of the original claim

We can conclude that we accept a golf club manufacturer claims that golfers can lower their scores by using the manufacturer’s newly designed golf clubs.