Part 1)
A physical therapists wishes to find out whether an exercise program rises flexibility. He measures the flexibility (in inches) of 12 randomly selected subjects both before and after intensive eight-week training program as well as obtains the following data:
Before: 18.5, 21.5, 16.5, 21, 20, 15, 19.75, 15.75, 18, 22, 15, 20.5
After: 19.25, 21.75, 16.5, 20.5, 22.25, 16, 19.5, 17, 19.25, 19.5, 16.5, 20
(a) why is this a matched - pairs?
(b) Test the claim that the flexibility before exercise program is less than the flexibility after exercise program at the significance level of 0.02. Note: the data is approximately normal with no outliers.
(c) Using the data from previous problem, develop a 95% confidence interval regarding the population mean difference. Interpret your result.