An investigator wished to determine whether epinephrine has the e ffect of elevating plasma cholesterol levels in humans. Twelve adult males were selected and given both a placebo and the drug. Blood samples were taken following injection of the placebo and again after injection of epinephrine. Analysis of the blood samples resulted in the following data:
Cholesterol Levels (mg/100mL)
subject placebo epinephrine
1 178 184
2 240 243
3 210 210
4 184 189
5 190 200
6 181 191
7 156 150
8 220 226
9 210 220
10 165 163
11 188 192
12 214 216
(a) Formulate an appropriate statistical model, defi ning all the terms. State the null and two-sided alternative hypotheses which reflect the research question of interest.
(b) Enter the data into R, and calculate the means for placebo and epinephrine. Find a 95% confi dence interval for the mean diff erence in cholesterol levels between the placebo and epinephrine. Use the confi dence interval to test your null hypothesis.
(c) Would a 99% confi dence interval contain zero? Briefly explain.
(d) Perform a test which addresses the research question but makes no assumption about the two populations being normally distributed. Compare the P-value for this test with the P-value found in (b). Comment on why one is substantially larger than the other.