Question

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

You begin your report to the Par, Inc. management team by offering the following hypothesis pair as a way of representing the problem.
H0 : μ1 - μ2 ≤ 0
H1 : μ1 - μ2 > 0

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.

Answer 1

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.

Explanation:

Given that :

μ1=population mean driving distance for the current golf ball

μ2=population mean driving distance for the new golf ball

H0 : μ1 - μ2 ≤ 0

H1 : μ1 - μ2 > 0

The Null hypothesis assumes that the average driving distance of the current golf ball is less than or equal to the average driving distance of the current golf ball

For the Alternative ; If there is significant evidence that the average driving distance of the current golf ball is greater or longer than the average driving distance of the new golf ball ;then we reject our initial claim (the Null hypothesis).