Par, Inc. You have been retained by Par, Inc., a major manufacturer of golf equi

Question

Par, Inc.

You have been retained by Par, Inc., a major manufacturer of golf equipment, to offer consultation about a new product that is currently under development. Management believes that Par's market share can be increased with the introduction of a new cut-resistant, longer-lasting golf ball. The research group at Par has been investigating a new golf ball coating. The new coating has been designed to resist cuts, leading to a more durable product. So far, the durability tests have been promising.

One of the researchers on your team has voiced concerns about the effects of the new coating on the performance of the new golf ball. Par would like the new cut-resistant ball to offer driving distances comparable to those of the current-model golf ball. The average driving distance for the new golf ball can be equal to or longer than the current model, but not shorter.

To compare the driving distances for the two models, you arranged an experiment in conjunction with the Par research team. Forty golf balls of each type were subjected to driving-distance tests. You offered the idea of testing the driving distance with a mechanical hitting machine to isolate any mean differences in the distances to the two model golf balls themselves. The results of the tests, with distances measured to the nearest yard, follow.

Let

1=population mean driving distance for the current golf ball

2=population mean driving distance for the new golf ball

Near the end of your presentation, an executive for Par, Inc. asks you the following question, “Assuming the same sample of golf balls, what would the average distance difference have to exceed for you to make the opposite recommendation?”

1) Find the answer to her question using the information in the Excel output above and the following equation:

A) 2.775 yards
B) 3.980 yeards

C) 3.478 yeards
D) 4.103 yards

You begin your report to the Par, Inc. management team by offering the following hypothesis pair as a way of representing the problem.

2)How would you explain these hypotheses to the management team?

A) We assume that the current model ball has an average driving distance that is greater than the new cut-resistant ball. However, if the new model has a mean driving distance that is greater than or equal to the current model, then we should reject our assumption.

B)We assume that the driving distances for the current model and the new model are equal. If the driving distances between the current and new models are very far apart, then we should reject our assumption.

C)We assume that the current golf ball has an average driving distance that is greater than or equal to that of the new model ball. However, if the new model has a mean driving distance that is significantly longer, then we should reject our assumption.

D)We assume that the new golf ball has an average driving distance that is greater than or equal to that of the current ball. However, if the current model has a mean driving distance that is significantly longer, then we should reject our assumption.

3) In the graphs above, the lighter blue color represents the non-rejection region for the null hypothesis while the darker blue color represents the rejection region.

Decision time. You must now make a decision about whether to reject your null hypothesis or fail to reject your null hypothesis and present your finding to the Par, Inc. research team. As their consultant, your decision must be 1) correct, and 2) explained in “plain English” so that everyone within Par, Inc. can understand your recommendation and why.

A)Reject H0 because the p-value is less than = .05. In my analysis, since the p-value is less than = .05, the t-statistic falls to the right of the t-critical value, placing it in the rejection region. There is evidence to support the conclusion that the current golf ball outdistances the new model substantially, bringing the new coating into question. I recommend stopping development of the new cut-resistant golf ball at this time.

B)Fail to reject H0 because the p-value is greater than = .05. In my analysis, since the p-value is greater than = .05, the t-statistic falls to the left of the t-critical value, placing it in the non-rejection region. There is evidence to support the conclusion that the current golf ball and the new model do not differ significantly in their average drive distance. I recommend continuing development of the new cut-resistant golf ball at this time.

C)Fail to reject H0 because the p-value is greater than = .05. In my analysis, since the p-value is greater than = .05, the t-statistic falls to the left of the t-critical value, placing it in the rejection region. There is evidence to support the conclusion that the current golf ball outdistances the new model substantially, bringing the new coating into question. I recommend stopping development of the new cut-resistant golf ball at this time.

D)Reject H0 because the p-value is greater than = .05. In my analysis, since the p-value is greater than = .05, the t-statistic falls to the left of the t-critical value placing it in the non-rejection region. There is evidence to support the conclusion that the new golf ball outdistances the current model substantially. I recommend continuing development of the new cut-resistant golf ball at this time.

4) In the graphs below, the lighter blue color represents the non-rejection region for the null hypothesis while the darker blue color represents the rejection region. Based on the null and alternative hypotheses and Excel output above, which graph would be the correct one to use in your presentation to Par's management team?

A)

B)

C)

D)

Explanation / Answer

1. option A difference =2.775

2. D)We assume that the new golf ball has an average driving distance that is greater than or equal to that of the current ball. However, if the current model has a mean driving distance that is significantly longer, then we should reject our assumption.

3. D)Reject H0 because the p-value is greater than = .05. In my analysis, since the p-value is greater than = .05, the t-statistic falls to the left of the t-critical value placing it in the non-rejection region. There is evidence to support the conclusion that the new golf ball outdistances the current model substantially. I recommend continuing development of the new cut-resistant golf ball at this time.

4. C graph

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