An organizational psychologist wants to know if workers' health would improve if a company gave workers extra days off. All workers take a standard physical exam twice a year and are given an overall health rating with higher scores indicating better health. The psychologist selected five workers at random, arranged to have them receive an additional 2 days off every month over the period between health exams, and then compared the health scores on the two exams. Using the .05 significance level, do the scores in the table below support the notion that having extra days off improves health?
Health Rating Before and After Period of Extra Days Off
Worker Before After
A 75 81
B 66 67
C 44 46
D 86 88
E 89 89
a. Use the five steps of hypothesis testing.
b. Sketch the distributions involved.
c. Figure the effect size and find the approximate power of this study.
d. Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample, including understanding decision errors, effect size and power, but who knows nothing about t tests of any kind (for example, you do not need to describe the steps or logic of hypothesis testing). Be sure you explain how this problem differs from a problem with a known population variance and a single sample. Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.
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