Question

A pharmaceutical company is trying to show that its cancer drug is effective. To meet the regulatory standards it must show that it stops or slows tumor growth in at least 30 percent of patients at a five percent significance level. Suppose the drug is truly effective and would in fact stop or slow tumor growth in 35 percent of all patients. If the company tests this drug on a random sample of 85 patients what is the probability of making a Type II error? (Answer as a probability, not a percent. Record your answer accurate to at least the nearest second decimal place with standard rounding.)

Answer 1

hypothesized proportion po=		0.3
true proportion pa=		0.35
sample size n=		85
standard error of po=√(po*(1-po)/n)=		0.0497
standard error of pa=√(pa*(1-pa)/n)=		0.0517
0.05 level and right tailed test critical value Zα=1.645
rejection reg:p̂ >=po+Zα*σpo or p̂ >		0.3815

type II error=β=P( p̂ <0.3815|p=0.35)=P(Z<(0.3815-0.35)/0.0517)=P(Z<0.61)=0.7291~ 0.73