A dietitian wishes to compare the effect of mineral supplements on the cholesterol levels of his patients. Six randomly selected patients were pretested for cholesterol and given mineral supplement for 6 weeks and then tested for cholesterol. The results are given below:

subject	1	2	3	4	5	6
Before	220	215	248	180	192	344
After	210	180	220	178	183	328

a. Find the differences in the cholesterol levels, Di's and compute the mean, X_Dbar

and the std. deviation, S_D of the differences

b. Construct a box-plot for the differences and comment on the result

c. Find a 95% confidence interval estimate for D (difference in the true mean cholesterol levels before and after the mineral supplement)

d. Is there sample evidence to conclude that the mineral supplement reduces the cholesterol level? Test at =0.05; write the hypotheses, compute the test statistic & P-value, make a decision, and write a summary

2. Write about the sampling distribution of the mean of the differences, X_Dbar

mentioning all essential points