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 μ1=population mean driving distance for the current golf ball
μ2=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:
T=(x1-x2)-D0 / √ S1^2/n1+S2^2/n2
A) 2.775 yards
B) 3.980 yeards
C) 3.478 yeards
D) 4.103 yards