Homework Solutions 11

Homework Solutions 11 - (W4150 Intro to Probability and...

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Solutions to Homework #11 (W4150 ‘Intro to Probability and Statistics’, S04) Sec. 10.12. (1) H 0 : p = .4 H 1 : p > .4 α = .05 If we denote the number of those who choose lasagne by X then under H 0 X ~ binomial(20;.4) and so P-value is given by P[X > 9 | p = .4] = 1 – P[X < 8 | p = .4] = .4044 > .05 Therefore we cannot reject null-hypothesis. Sec.10.12. (2) H 0 : p = .4 H 1 : p > .4 α = .05 Let’s denote the number of those who favored capital punishment by X. Then under H 0 X ~ binomial(15;.4) and so P-value is given by P[X > 8 | p = .4] = 1 – P[X < 7 | p = .4] = = .2131 > .05 Therefore we cannot reject null-hypothesis. Sec. 10.12. (6) H 0 : p = .25 H 1 : p > .25 α = .05 Since n = 90 > 30 we’d like to use normal approximation for binomial distribution here. μ = np = 22.5; σ = npq = 4.107 and critical region is defined as X > 28 where X is the number of students using bicycles. Therefore critical value of Z is z = (28.5 – 22.5)/(4.107) = 1.43 and P[X > 28] = P[Z > 1.43] = 1 - .9236 = .0724 > .05 formally we cannot reject H 0 ; however, relatively low P-value clearly indicates that there is some evidence in favor of alternative hypothesis. Sec. 10.12 (9) H 0 : p 1 = p 2 H 1 : p 1 p 2 , where p 1 is proportion of urban residents and p 2 – proportion of suburban residents who favor the nuclear plant. Following Example 10.12 we compute
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Homework Solutions 11 - (W4150 Intro to Probability and...

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