A crossover study was conducted to investigate whether oat bran cereal helps to lower cholesterol levels in hypercholesterolemic males. Fourteen such individuals were randomly placed on a diet that included either oat bran or corn flakes; after two weeks, their low-density lipoprotein (LDL) cholesterol levels were recorded. Each man was then switched to the alternative diet. After a second two-week period, the LDL cholesterol level of each individual was again recorded. The data from this study are shown below:
subject corn flakes LDL oat bran LDL
1 4.61 3.84
2 6.42 5.57
3 5.40 5.85
4 4.54 4.80
5 3.98 3.68
6 3.82 2.96
7 5.01 4.41
8 4.34 3.72
9 3.80 3.49
10 4.56 3.84
11 5.35 5.26
12 3.89 3.73
13 2.25 1.84
14 4.24 4.14
a. Are the two samples paired or independent?
b. What are the appropriate null and alternative hypotheses for a two-sided test?
c. Conduct the test at the 0.05 level of significance. What is the p-value?
d. What do you conclude?