Case Study Below is the Problem statement Par, Inc., is a major manufacturer of golf equipment. Management believes that Par’s 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. To compare the driving distances for the two balls, 40 balls of both the new and current models were subjected to distance tests. The testing was performed with a mechanical hitting machine so that any difference between the mean distances for the two models could be attributed to a difference in the two models. The results of the tests, with distances measured to the nearest yard, follow. These data are available on the website that accompanies the text.
Managerial Report 1. Formulate and present the rationale for a hypothesis test that Par could use to compare the driving distances of the current and new golf balls. 2. Analyze the data to provide the hypothesis testing conclusion. What is the p-value for your test? What is your recommendation for Par, Inc.? 3. Provide descriptive statistical summaries of the data for each model. 4. What is the 95% confidence interval for the population mean driving distance of each model, and what is the 95% confidence interval for the difference between the means of the two populations? 5. Do you see a need for larger sample sizes and more testing with the golf balls? Discuss.
Solution: Par, Inc. is a major manufacturer of golf equipment and they want to introduce a cut-resistant and longer lasting golf ball. Though, the result of test on the durability of the improved product another issue has been raised – and and this is the effect of the new coating on driving distances.
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40 balls of both the new and current models were subjected to distance test.
Our hypothesis test is Ho: µ1 - µ2 = 0, against Ha: µ1 - µ2 ≠ 0. Just by looking at the descriptive statistics for each model, we can initially conclude that Current model has a longer range of distance based on the 40 samples with a mean of 270.275 compare to 267.500 for new model. To test further our hypothesis, we set set our at .05 and our rejection criteria is Reject Ho and and accept Ha if F > α Fc or P < (.05). Since our hypothesis test done thru stat tools doesn’t indicate Fc, we will use α the P-value approach. And based on the p-value of 0.0940, we cannot reject Ho, there is no significant evidence that New and current model driving distances are different. And to support our hypothesis test, we also perform interval confidence for both model. There is 95% probability that the true population mean is between 267.47 and 273.07 (current model) while 264.33 and 270.66. And by their confidence intervals, we can say that there is no significance difference between the driving distances of Current Model and New Model. And also because of this, larger sample size is not anymore required as it will also generate same conclusion. Our recommendation is for the company (Par, Inc.) to continue with further study of the improved cut-resistant, longer lasting golf ball. But ofcourse, Par, Inc. should also consider other factors like costing, availability of suppliers and the like before finalizing and l aunching the product.
