The president of a large company is in the process of deciding whether to adopt

Question

The president of a large company is in the process of deciding whether to adopt a lunch- time exercise program. The purpose of such pro- grams is to improve the health of workers and, in so doing, reduce medical expenses. To get more information, he instituted an exercise program for the employees in one office. The president knows that during the winter months medical expenses are relatively high because of the incidence of colds and flu. Consequently, he decides to use a matched pairs design by recording medical expenses for the 12 months before the program and for 12 months after the program. The “before” and “after” expenses (in thousands of dollars) are compared on a month-to-month basis and shown here. Do the data indicate that exercise programs reduce medical expenses .

Hypothesis: H0: Ud = 0 H1: Ud > 0 Match pairs.

Can you explain why the alternative hypothesis is greather than 0. Shouldn't it be less than 0

Explanation / Answer

Here, mu1 is the mean expense before the program and mu2 is the mean expense after the program

Hence, mud = mu1 - mu2

As we want to perform the hypothesis test to know whether medical expenses have decreased

Hence, alternative hypothesis is mud >0

As you are mentionting this should be less than it would be possible when we consider mud = mu2 - mu1

but, generally mud = mu1 - mu2

Hence, given alternative hypothesis is correct

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