The risk manager of your firm is attempting to determine if her recently instituted luncheon exercise program has made a difference in health care expenses. She has gathered information about the firm's medical expenses for twelve individuals who have joined her program. These information are provided in the table below:
Individual Linda Kim Sarah Matthew Jesse Nathan Karen Ruth Tina Gary Fred Jayson
BPE 68 44 30 58 35 33 52 69 23 69 48 26
AJE 59 42 20 62 25 30 56 62 25 75 40 26
a. Construct a 95% confidence interval for the difference between the medical expenses before and after joining the program.
b. At the 5% level of significance, has the program reduced the monthly medical expenses? (show all work)