Homework Solutions 10 - (W4150 Intro to Probability and...

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Solutions to Homework #10 (W4150 ‘Intro to Probability and Statistics’, S04) Sec. 10.4. (1) (a) Conclude that fewer than 30% of the public are allergic to some cheese products when in fact 30% or more are allergic. (b) Conclude that at least 30% of the public are allergic to some cheese products when in fact fewer than 30% are allergic. Sec.10.4. (2) (a) The training is effective (b) The training is effective Sec. 10.4. (3) (a) The firm is not guilty. (b) The firm is guilty. Sec.10.4 (6) (a) α = P{to reject H o when it’s true} = P(X< 3 | p=.6) = .0548 following the binomial distribution (b) For three different alternative values we have: β = P{to accept H 0 when it’s not true} = P(X>3|p=.3) = .3504 β = P(X>3|p=.4) = .6177 β = P(X>3|p=.5) = .8281 Sec. 10.4. (7) Here we apply the normal approximation to the binomial (since n is large enough): (a) α = P{to reject H o when it’s true} = P(X<24 | p=.6) = P[Z<(24.5-(.6)(50))/ (50)(.4)(.6)} = P(Z< -1.59) = .0559 (b) For three different alternative values we have: β = P{to accept H 0 when it’s not true} = P(X>24|p=.3) = P(Z>2.93) = .0017 β = P(X>24|p=.4) = .0968 β = P(X>24|p=.5) = .5557 Sec. 10.4. (12) (a) p = .6, n = 400; therefore μ = np = 240 and σ = 400(.6)(.4) = 9.798
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