Question

A researcher is conducting a randomized, placebo-controlled experiment to test the hypotheses H0:p1=p2 versus Ha:p1>p2H_a: p_1 > p_2Ha​:p1​>p2​ where p1= the population proportion of all patients given the new drug who are cured and p2=the population proportion of all patients given the placebo who are cured. The patients were randomly assigned to the two treatment groups in a 2 to 1 ratio, that is, twice as many patients were randomized to the new treatment as were to the placebo group. At the end of the experiment, the researcher reports the sample proportions of patients that were cured as: \hat{p}1=0.5 and \hat{p}2=0.7 In computing the z test statistic for performing the hypothesis test, the researcher needs to first compute the estimate of the common population proportion of patients cured \hat{p}_c (appropriate to think about under the null hypothesis). Provide an estimate for this common population proportion.

Answer 1

Question asked: Provide an estimate for this common population proportion.

Given:

1 = 0.5

2 = 0.7

Let

Number of patients assigned to the placebo group = n2 = n.

Since twice as many patients were randomized to the new treatment as were to the placebo group.:

Number of patients assigned to the new treatment group = n1 = 2n.

So,

an estimate for this common population proportion is given by:

Substituting values, we get:

So,

Answer is:

0.5667