A crossover study was conducted to investigate whether oat bran cereal helps to lower serum choles- terol 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. LDL (mmol/l) Subject Corn Flakes Oat Bran 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 Questions; (a) What are the appropriate null and alternative hypotheses for a two-sided test? (b) What statistical test would be appropriate to test whether mean cholesterol levels on the two diets are significantly different from each other? Label and define the parameter(s) of interest. (c) Use R or Excel to conduct the test at the 0.05 level of significance. What is the p-value? (Include relevant output), Construct a 95% confidence interval of the difference
A crossover study was conducted to investigate whether oat bran cereal helps to lower serum choles-
terol 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.
LDL (mmol/l)
Subject Corn Flakes Oat Bran
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
Questions;
(a) What are the appropriate null and alternative hypotheses for a two-sided test?
(b) What statistical test would be appropriate to test whether mean cholesterol levels on the two diets are significantly different from each other? Label and define the parameter(s) of interest.
(c) Use R or Excel to conduct the test at the 0.05 level of significance. What is the p-value?
(Include relevant output), Construct a 95% confidence interval of the difference.
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