Depression is one of the most commonly diagnosed conditions among hospitalized patients in mental institutions. The primary measure of depression is the CES-D scale developed by the Center for Epidemiologic Studies, in which each person is scored on a scale of 0 to 60. The following results were found for a group of randomly selected women: n = 200, x = 10:4, and s = 10:3.
A study is now considered to investigate the effect of a new drug aimed at lowering anxiety among hospitalized patients in similar mental institutions. Subjects would be randomized to receive either the new drug or placebo, then averages of CES-D scores will be compared using the two-sided two-sample t test at the 5% level. How large should the total sample size be if it is important to detect a CES-D score reduction of 3.0 with a power of 90%?