A study tested whether serum cholesterol was reduced after using a certain brand of margarine as part of a low fat, low cholesterol diet. The subjects consumed on average 2.31g of the active ingredient, stanol easter, a day. This data set margarine.csvcontains information on 18 people using margarine to reduce cholesterol over three time points (baseline, 4 weeks and 8 weeks).

Variable name	Variable
ID	Participant number
Before	Cholesterol before the diet (mmol/L)
After4weeks	Cholesterol after 4 weeks on the diet (mmol/L)
After8weeks	Cholesterol after 8 weeks on the diet (mmol/L)

1. Which t-test (one sample, two sample, or paired) would be most appropriate to answer to test to see if cholesterol levels changed from baseline after being on the margarine diet for 8 weeks? Justify your response. (5 points)

1. Write the null and alternative hypothesis in words.(6 points)

Suppose we had rejected the null hypothesis and concluded that cholesterol levels were lower after 8 weeks, but subsequent testing in a much larger sample subsequently showed that there really was no significant difference. If this had occurred, what type of statistical error would we have made based on the first (small) sample, a type I or type II error?(5 points)