Question

Par, Inc. is a major manufacturer of golf equipment. Management believes that Pars market share could be increased with the introduction of a cut-resistant, longer-lasting golf ball. Therefore, the research group at Par has been investigating a new golf ball coating designed to resist cuts and provide a more durable ball. The tests with the coating have been promising. One of the researchers voiced concern about the effect of the new coating on driving distances. Par would like the new cut-resistant ball to offer driving distances comparable to those of the current-model golf ball. What kind of kind of study should Par design to compare the driving distances of the current and new golf balls and why?

Things to Consider:

• What should be the sample size?
• Who would hit the balls to calculate the driving distance?
• What kind of hypothesis test would you set up?
  • Should it be a one-parameter or two-parameter test?
  • Should it be a t-test or z-test?
  • Should it be a one-sided or two-sided test?

Answer 1

In order to study the driving distances of the cut resistant version of golf ball, take a sample of atleast size 30 and make a professional golfer to hit those balls and measure their driving distances.

Let new denote the mean driving distance for the new ball and old denote the mean driving distance for the older version.

The hypotheses are:

H0: new =  old

Ha: new >  new

So it is a one parameter test.

Since there is plenty of data regarding driving distances of golf balls, it is better to conduct a z-test because the standard deviation of the population will be known to us beforehand.

It will be a one sided test, as is visible from the alternative hypothesis.