We\'re comparing middle aged executives. Some exercise regularly, others are cou

Question

We're comparing middle aged executives. Some exercise regularly, others are couch potatoes. After running on a treadmill for 6 minutes, their heart rates were compared:

Exercise group 99 119 122 111 115 113 103 100 78 100

Couch potatoes 120 130 108 129 115 111 127 102 118 140

Carry out a complete test to see if there is a difference in heart rates between the two groups. Note that I'm not telling you what test to use, or what level of to pick. It is entirely up to you how to proceed. Reminders: you should check your assumptions before you pick a test; you should decide whether or not to use a one sided test; you should explain if the data are paired or not (and why). Make sure you provide thorough explanations for everything you do.

Explanation / Answer

We are checking if there is a difference and not necessarily if one is bigger than the other. Hence do a two tailed test for checking equality vs not equal.

The data are not paired as the same person is not doing a couch potato and then doing exercise. They are completely different people and they are not doing against each other simultaneously. Hence it is unpaired data.

Let the average heart rate of exercise group is ex bar and that of couch potato be cp bar

Null hypothesis, H0: ex bar= cp bar

Alternate hypothesis, H1: ex bar != cp bar

do a two tailed t-test as we don't have 25 observations each for z-test

Exercise Couch DIFF, d (d-dbar)^2 99 120 -21 49 119 130 -11 9 122 108 14 784 111 129 -18 16 115 115 0 196 113 111 2 256 103 127 -24 100 100 102 -2 144 78 118 -40 676 100 140 -40 676 avg -14

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