Suppose that a new drug is tested on a sample of n = 60 cancer patients. The new

Question

Suppose that a new drug is tested on a sample of n = 60 cancer patients. The new drug is to be compared to a placebo to see if it is better than the 20% cure rate of a placebo. A placebo is a fake drug treatment. If the drug is in fact no better than a placebo what is the probability that over 30% of the patients will report improvement? If the drug is in fact no better than a placebo what is the probability that under 25% of the patients will report improvement If the drug is in fact no better than a placebo what is the probability that between 10% and 18% will report improvement?

Explanation / Answer

p=0.20

here std error of proportion =(p(1-p)/n)1/2 =0.0516

a)P(X>0.30)=1-P(X<0.30)=1-P(Z<(0.3-0.2)/0.0516)=1-P(Z<1.9365)=1-0.9736=0.0264

b)P(X<0.25)=P(Z<(0.25-0.2)/0.0516)=P(Z<0.9682)=0.8335

c)P(0.1<X<0.18)=P(-1.9365<Z<-0.3873)=0.3493-0.0264=0.3229

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