A researcher working at a particular company wants to know if workers' health would improve if they were given extra days 'off. In this company, all workers undergo a standard physical exam twice a year and after each exam an overall health rating (higher scores mean better health) is automatically provided to the company. To conduct the study, the researcher selected five workers at random. She then arranged to have these five workers receive an additional 2 days off every month over the period between health exams. She then compared the health scores on the two exams. Do the results shown in the table below support the notion that extra days off improves health? (Use the .05 level.) Health Rating, Before and After Period of Extra Days Off 5 Worker Before After
WORKER BEFORE AFTER
A 75 81
B 66 67
C 44 46
D 86 88
E 89 89
(a) Define the parameter of interest and state null and research hypotheses.
(b) Determine the characteristics of the comparison distribution.
(c) What are the cut-off values for a test with significance level 0.05?