In a large experiment to determine the success of a new drug, 400patients with a

Question

In a large experiment to determine the success of a new drug, 400patients with a certain
disease are to be given the drug. If more than 300 and less than340 patients are cured. We
shall conclude that drug is over 80% effective. Find theprobability of committing a type I
error. What is the probability of a type II error () error Ifthe new drug is only 70% effective.
(Hint: Use the normal approximation to the Binomial)

Explanation / Answer

n=400 p=.8, q=.2 =np=320 =npq=64=8 P(300>y or y>340)=ans , where y is binomial with =320and =8 ans=2P(y>340) by symmetry Let x be normal with with =320 and =8 ans= 2P(x>339.5)=2P(z>(339.5-320)/8)= 2P(z>2.4375) where zis standarnd normal ans= 2(.5-.4927)=.0146= = P(300

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