Question

2. Benjamin Franklin wrote ...early to rise makes a man healthy, wealthy, and wise." Recent research may cast doubt on the healthy part. Researchers at the University of Westminster, London, studied the saliva of 42 volunteers. The test subjects were randomly divided into two groups. One group woke up between 5:30 am and 7:00 am; another group woke up between 7:00 am and 10:30 am. The amount of cortisol in the saliva of all volunteers was measured. Cortisol is a hormone that affects tempe and concentration. The data are summarized below. rament Early risers: 19, 203.1 1 28.2 Late risers: n-23, 12 = 251.8, s2-26.7 (a) 6 points. Calculate a 95% confdence interval for the difference between average cortismounts in saliva of early and late risers (b) 3 points. Cirele a letter that represents correct interpretation of the decision made in part (a). (A) we can state with 95% confidence that difference between average cortisol amounts in saliva (B) we can state with 95% confidence that difference between average cortisol amounts in saliva (c) 4 points. Based on your interval constructed in part (a), do the given data support Benjamin of early and late riser populations is in the interval constructed in part (a). of early and late riser samples is in the interval constructed in part (a) Franklin's claim? Explain
I caclulated the interval to be (-65.34,-31.5) for part A. Can you help me with part b and c. For C, please explain your reasoning behind your answer. Thanks!

Answer 1

b)

confidence interval is constructed to represent population not samples

so, answer is option A)

c)

since, confidence interval is negative, it means cortisol in the saliva of early riser is significantly less than that of late riser.
and hence, early riser are more healthy than that of late riser
So, there is enough evidence to support Benjamin Franklin's claim with 95% confidence