Question

A certain golf club manufacturer advertises that its new driver (the club you use to hit golf balls off the tee) will increase the distance that golfers achieve relative to their current driver. We decide to test this claim by having 15 golfers hit a drive using the new driver, and then hit one using their current driver. Here are the data for 15 people, with yardages using both clubs:

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
New	247	259	248	275	282	307	288	215	221	260	292	198	240	304	295
Current	240	254	238	268	275	301	292	197	203	262	281	189	225	297	274

a) Show a side-by-side boxplot of the driving distances for the current and new drivers as well as the difference between new and current drivers (a total of three boxplots, side-by-side. Conduct a paired t-test to test whether the new driver produces longer drives, on average, when compared to the current driver using .05 as the probability of a Type 1 error. State your hypotheses, and be sure to check the conditions for your test. State the P-value of your test. (Use R studio - and show commands and output for using R.)

b) By using a 95% confidence interval, estimate the true difference in length produced by the new driver relative to the current one, and explain what this confidence interval means in context of this problem.  (Use R studio - and show commands and output for using R.)

Answer 1

R code along with output is given below:

A)

Side by side boxplot is given above in R output

As we have to conduct paired test such that we can find out whether new drivers have mean greater than that of old ones.

So it is the right tailed test.

Hypothesis will be:

Where is the difference of new and old observations.

As we can see that in the output given above

P value =  9.568e-05 <

which implies that we have enough evidence to reject nul hypothesis.

i.e., mean of new drivers is more than as compare to that of old ones.

B)

As we can see in the output above

95% CI for the difference is given by:

Here as we can see that 0 is not there in the CI which means that here null hypothesis is rejected.