Chapter 8, Problem 148P

A study of genetic factors related to coronary heart disease (CHD) was performed as a substudy within the ARIC Study [20]. The data in Table 8.35 were provided by ethnic group for high-density lipoprotein (HDL) cholesterol (mg/dL).

Table 8.35 Mean HDL cholesterol (mg/dL) by ethnic group

Suppose a new study is conducted in which there will be n₁ Caucasian subjects and n₂ African American subjects, where n₂ = 2n₁. How large should n₁ and n₂ be in order for the new study to have 90% power to detect a mean difference of 5 mg/dL between the two groups, where a two-sided test is conducted with α = .05? (Hint: Assume that the standard deviations in the above table for each ethnic group are the true standard deviations.)