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Dr. Hackney STA Solutions pg 29

# Dr. Hackney STA Solutions pg 29 - 3-2 Solutions Manual for...

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3-2 Solutions Manual for Statistical Inference 3.5 Let X = number of effective cases. If the new and old drugs are equally effective, then the probability that the new drug is effective on a case is . 8. If the cases are independent then X binomial(100 , . 8), and P ( X 85) = 100 x =85 100 x . 8 x . 2 100 - x = . 1285 . So, even if the new drug is no better than the old, the chance of 85 or more effective cases is not too small. Hence, we cannot conclude the new drug is better. Note that using a normal approximation to calculate this binomial probability yields P ( X 85) P ( Z 1 . 125) = . 1303. 3.7 Let X Poisson( λ ). We want P ( X 2) . 99, that is, P ( X 1) = e - λ + λe - λ . 01 . Solving e - λ + λe - λ = . 01 by trial and error (numerical bisection method) yields λ = 6 . 6384. 3.8 a. We want P ( X > N ) < . 01 where X binomial(1000 , 1 / 2). Since the 1000 customers choose randomly, we take p = 1 / 2. We thus require
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