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. (Feel free to use R in showing your work - and show your commands and output if 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. (Feel free to use R in showing your work - and show your commands and output if using R.)

Answer 1

a)

Following is the R script to generate the box plots:

Following are the box plots:

--------------------------------------------

Hypotheses are:

Following is the R command to run paired t test:

Following is the otuput:

The p-value is 0.0001

Since p-value is less than 0.05 so we rejetc the null hypothesis.

Conclusion: There is evidence to conclude that the new driver produces longer drives, on average, when compared to the current driver using .05 as the probability of a Type 1 error.

b)

The command for confidence interval:

t.test(New, Current, paired = TRUE)

The 95% confidence interval from above output is

The requried confidence interval is ( 5.146, 12.854).

It shows that we are 95% confident that true difference  in length produced by the new driver relative to the current one lie in the above interval.