Question: Huamn beta-endorphin (HBE) is a hormone secreted by the pituitary gland under conditions of stress. A researcher conducted a study to investigate whether a program of regular exercise might affect the resting (unstressed) concentration of HBE in the blood. He measured blood HBE levels in January and again in May from 10 participants in a physical fitness program. The results were as follows:

Participant 1:

January:42

May: 22

Participant 2:

January: 47

May: 29

Participant 3:

January:37

May:9

Participant 4:

January:9

May:9

Participant 5:

January:33

May:26

Participant 6:

January:70

May:36

Participant 7:

January:54

May:38

Participant 8:

January: 27

May:32

Participant 9:

January: 41

May:33

Participant 10:

January: 18

May:14

Mean: 37.8 for January and 24.8 for May

Standard deviation: 17.6 for January and 10.9 for May

a) construct a 95% confidence interval for the population mean difference in HBE levels between January and May

b) interpret the confidence interval from part a. That is, explain what the interval tells you about HBE levels

c) Is there evidence that mean HBE levels are different in May than in January?

d) Use an appropriate test of hypotheses to answer part c