Chapter 10, Problem 116H

Use the following information to answer the next two exercises. A new AIDS prevention drug was tried on a group of 224 HIV positive patients. Forty-five patients developed AIDS after four years. In a control group of 224 HIV positive patients, 68 developed AIDS after four years. We want to test whether the method of treatment reduces the proportion of patients that develop AIDS after four years or if the proportions of the treated group and the untreated group stay the same.

Let the subscript t = treated patient and ut = untreated patient.

The appropriate hypotheses are:

a. $H_0:p_t<p_{ut}\text{and}{H}_a:p_t\ge p_{ut}$

b. $H_0:p_t\le p_{ut}\text{and}{H}_a:p_t>p_{ut}$

c. $H_0:p_t=p_{ut}\text{and}{H}_a:p_t\ne p_{ut}$

d. $H_0:p_t=p_{ut}\text{and}{H}_a:p_t<p_{ut}$