Question

1. Several baseline studies are conducted on X = “cholesterol level (mg/dL)” in a certain population of individuals. From the given information described below for each of these studies, choose the LETTER of the most appropriate statistical test to be implemented, from the following list. Note: For each study, there is only one correct choice of test. However, a given statistical test can be the correct choice for more than one study. For example, choice A could be the correct test for the studies in both parts (i) and (ii).

A = One-sample Z-test

B = One-sample t-test

C = Independent two-sample Z-test

D = Independent two-sample t-test

E = Paired Z-test

F = Paired t-test

G = Satterwaithe’s (approximate t-) test

H = Wilcoxon Signed Rank Test

I = Wilcoxon Rank Sum Test

J = Chi-squared Test

K = McNemar’s Test

L = F-test

M = Kruskal-Wallis Test

N = None of the Above

(i) We wish to determine if the mean cholesterol level of the population is significantly different from 240 (high). A random sample of 500 individuals is selected, and a dotplot shows that the cholesterol levels are approximately normally distributed.

(ii) We wish to determine if the mean cholesterol levels of men and women in the population are significantly different. A random sample of 250 men and 250 unrelated women are selected for comparison. A dotplot shows that the cholesterol levels of each group are approximately normally distributed.

(iii) We wish to determine if the mean cholesterol levels of men and women in the population are significantly different. A random sample of 25 men and 25 unrelated women are selected for comparison. A dotplot shows that the cholesterol levels of each group are approximately normally distributed, with approximately equal sample variances.

(iv) We wish to determine if the mean cholesterol levels of men and women in the population are significantly different. A random sample of 25 men and 25 unrelated women are selected for comparison. A dotplot shows that the cholesterol levels of each group are approximately normally distributed, but with significantly different sample variances.

(v) We wish to determine if the mean cholesterol levels of men and women in the population are significantly different. A random sample of 25 men and 25 unrelated women are selected for comparison. A dotplot shows that the cholesterol levels of each group are not normally distributed, but highly skewed.

(vi) We wish to determine if the mean cholesterol levels of husbands and their wives in the population are significantly different. A random sample of 250 married couples is selected for comparison between corresponding spouses. A dotplot shows that the cholesterol levels of each group are approximately normally distributed.

(vii) We wish to determine whether or not there is a significant difference between the proportions of men and women with high cholesterol (X >= 240) . A random sample of 10 men and 10 unrelated women are selected; each individual is then classified according to whether or not he/she has high cholesterol, for eventual comparison.

(viii) We wish to determine whether or not there is a significant difference between the proportions of husbands and their wives with high cholesterol (X >= 240) . A random sample of 250 married couples is selected; each spouse in every couple is then classified according to whether or not he/she has high cholesterol, for eventual comparison.

(ix) We wish to determine whether or not the difference between the proportions of men and women with high cholesterol (X >= 240) in the population, is equal to 10%. A random sample of 250 men and 250 unrelated women are selected; each person is then classified according to whether or not he/she has high cholesterol, for eventual comparison.

(x) We wish to determine whether there is a significant difference between the proportions of individuals in the population whose cholesterol level is low (X < 200), normal (200 <= X <= 239) , or high (X >= 240) . A random sample of 500 individuals is selected; each individual is then classified for eventual comparison.

Answer 1