Question

A golf equipment manufacturer would like to convince members of a club that its golf balls travel farther than those of a rival. For the comparison, twelve golfers were randomly selected from the club to each drive a ball from this manufacturer and from the rival. The results show the distance traveled, in yards. The complete set of results is provided below:

Should every golfer hit the rival ball first and then the manufacturer’s ball second? Explain your answer.

State the null hypotheses, paste the test output, and state your decision.

What is the 95% confidence interval for the mean difference? Interpret the confidence interval.

What assumption(s) was (were) required to perform this hypothesis test?

Does (do) the assumption(s) appear to be reasonably met in this case? Paste the Minitab output required to answer this question here.

Comment on the source of sampling error and a potential source of non-sampling error for this study (be specific).

Rather than have each golfer hit one ball of each type, the manufacturer could have easily chosen 12 more golfers and allowed all 24 golfers to hit one ball. Should the manufacturer run the study as it did (12 golfers hitting each type of ball) or with 24 golfers hitting just one randomly assigned ball? Justify your answer.

The complete set of results is provided below:

Golfer	Distance (manuf)	Distance (rival)
1	188	194
2	240	241
3	235	210
4	176	185
5	234	211
6	160	149
7	240	225
8	241	227
9	239	204
10	251	255
11	185	185
12	166	151

Answer 1

A golf equipment manufacturer would like to convince members of a club that its golf balls travel farther than those of a rival. For the comparison, twelve golfers were randomly selected from the club to each drive a ball from this manufacturer and from the rival. The results show the distance traveled, in yards. The complete set of results is provided below:

Should every golfer hit the rival ball first and then the manufacturer’s ball second? Explain your answer.

State the null hypotheses, paste the test output, and state your decision.

Difference = manuf-rival

We are testing manufacturer s golf balls travel farther than those of a rival.

This is upper tail test

Paired T-Test and CI: manuf, rival

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
manuf	12	212.92	34.49	9.96
rival	12	203.08	32.57	9.40

Estimation for Paired Difference

Mean	StDev	SE Mean	95% Lower Bound for μ_difference
9.83	13.88	4.01	2.64

µ_difference: mean of (manuf - rival)

Test

Null hypothesis	H₀: μ_difference = 0
Alternative hypothesis	H₁: μ_difference > 0

T-Value	P-Value
2.45	0.016

Calculated t=2.45, P=0.016 which is < 0.05 level of significance, Ho is rejected.

We conclude that manufacturer s golf balls travel farther than those of a rival.

What is the 95% confidence interval for the mean difference? Interpret the confidence interval.

Estimation for Paired Difference

Mean	StDev	SE Mean	95% CI for μ_difference
9.83	13.88	4.01	(1.01, 18.65)

µ_difference: mean of (manuf - rival)

we are 95% confidence that mean difference of all balls travel distance between the manufacturer and rival falls in the interval (1.1, 18.65).

What assumption(s) was (were) required to perform this hypothesis test?

The data is random, pairs are independent and the difference of distance is normally distributed.

Does (do) the assumption(s) appear to be reasonably met in this case? Paste the Minitab output required to answer this question here.

The normality plot shows there is no violation of assumptions.

The Kolmogorov–Smirnov test (KS test) shows the p value of the test = 0.150 which is > 0.05 level.

The normality assumptions are not violated.

Comment on the source of sampling error and a potential source of non-sampling error for this study (be specific).

Rather than have each golfer hit one ball of each type, the manufacturer could have easily chosen 12 more golfers and allowed all 24 golfers to hit one ball. Should the manufacturer run the study as it did (12 golfers hitting each type of ball) or with 24 golfers hitting just one randomly assigned ball? Justify your answer.

The manufacturer run the study as it did (12 golfers hitting each type of ball) because the variation between golfers is less compared ( within subject design) to 24 golfers study (between subject design).