To study the difference in drug therapy adherence among subjects with depression who received usual care and those who received care in a collaborative care model was the goal of a study conducted by Finley et al. (2003). The collaborative care model emphasized the role of clinical pharmacists in providing drug therapy management and treatment follow-up. Of the 50 subjects receiving usual care, 24 adhered to the prescribed drug regimen, while 50 out of 75 subjects in the collaborative care model adhered to the drug regimen.

Please answer the following:

1. Find the 90% confidence interval for the usual care group.

2. Find the probability of finding a difference in those receiving drug therapy vs. those receiving usual care that exceeds 20%.

3. Find the 95% confidence interval for the difference in those receiving drug therapy vs. those receiving usual care.