7.30. A clinical psychologist wants to choose between two therapies for treating mental depression. For six patients, she randomly selects three to receive therapy A, and the other three receive therapy B.

She selects small samples for ethical reasons;

if her experiment indicates that one therapy is superior, that therapy will be used on her other patients having these symptoms. After one month of treatment, the improvement is measured by the change in score on a standardized scale of mental depression severity. The improvement scores arc 10, 20, 30 for the patients receiving therapy A, and 30, 45, 45 for the patients receiving therapy B.

(a) Using the method that assumes a common standard deviation for the two therapies, show that the pooled s - 9.35 and se - 7.64.

(b) When the sample sizes arc very small, it may be worth sacrificing some confidence to achieve more precision. Show that the 90% confidence interval for (^2 - Pi) is (3.7, 36.3).

Interpret.

(c) Estimate and summarize the effect size.