Statistical Inference About Means and Proportions
with Two Populations
Case Problem: Par, Inc.
This case can provide discussion and differing opinions as to what hypothesis test should be conducted. Students should begin to see that logical arguments exist for structuring the hypotheses differently. In some interpretations of the problem, a two - tailed test can be appropriate for Par, Inc. In other interpretations of the same problem, a one - tailed test may be preferred. We suggest accepting different formulations of the Par, Inc. hypothesis test provided convincing rationale is provided.
1 = the population mean driving distance for the current golf ball
2 = the population mean driving distance for the new golf ball,
we suggest the following hypothesis test:
H0: 1 - 2 0
Ha: 1 - 2 > 0
This formulation is based on the information that the new golf ball is being designed to “resist cuts and yet still offer good driving distances.” The research hypothesis is not to prove the new golf ball out distances the current golf ball. In fact, Par could claim an improved quality with the cut resistance improvement provided the new golf ball has the same or better driving distance. The hypotheses have been structured so that rejection of H0 corresponds to the conclusion that the new golf ball has the lower mean driving distances; this conclusion indicates that the cut resistance advantage may be offset by the loss of distance.
The sample mean for the current golf ball was...