A new treatment has been developed for acquired immune deficiency syndrome (AIDS

Question

A new treatment has been developed for acquired immune deficiency syndrome (AIDS) A small clinical trial is to be performed in order estimate p, the population proposition of positive responders to the treatment. Before beginning the study, researchers want to know how many subjects should be involved if they desire a standard error no more than 0.05 Based on previous studies, their best guess of the proportion of people that respond to Determine how many subjects are needed for this study. Suppose the researchers used the number of subjects found in Part A and 25% of them responded positively to the treatment. Construct a 95% confidence interval for the true population proportion of positive responders Interpret your interval for Part B in context of the problem.

Explanation / Answer

(A)

SE = 0.05

sqrt(pq/n) = 0.05

pq/n = 0.0025

n = 0.2*0.8/0.0025 = 64

Hence subjects needed for the study are 64.

(B)

pcap = 0.25

For 95% CI, z value = 1.96

lower limit = 0.25 - 1.96*0.05 = 0.152

upper limit =  0.25 + 1.96*0.05 = 0.348

Hence CI = (0.152, 0.348)

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