2. To test the null hypothesis pi = P2 with two independent samples of sizes nį and n2, we require that n1 < N1/20, that n2 < N2/20, that n1 * pi * (1 – p1) > 10, and that n2 * p2 * (1– p2) > 10. Our test statistic TS is pi – p2 Va•(1 – p) • (+ + +) where p is the pooled estimate p = (x1 + x2)/(n1 + n2). (a) For a two-tailed test, we may compute +za/2 = ±InvNorm(a/2,0, 1) and check that the test-statistic falls in a tail. Or we may instead compute P = 2 * normalcdf (|TS|, 0,0, 1) and check that P < a. Suppose our null hypothesis is pi p2, that our sample sizes are ni = 1500 and n2 = 1600, and that we find x1 = 506 and x2 = 692. Assume that N1 and N2 are very large. i. If we use a two-tailed test, what is our alternative hypothesis: pi + p2 ? pi < P2 ? or pi > P2 ? ii. What would we conclude if we rejected the null hypothesis with a two-tailed test? iii. Can we reject the null hypothesis at level of significance a = 0.05, using a two-tailed test? iv. Can we reject the null hypothesis at level of significance a = 0.01, using a two-tailed test?

2. To test the null hypothesis pi = P2 with two independent samples of sizes nį and n2, we require that n1 < N1/20, that n2 < N2/20, that n1 * pi * (1 – p1) > 10, and that n2 * p2 * (1– p2) > 10. Our test statistic TS is pi – p2 Va•(1 – p) • (+ + +) where p is the pooled estimate p = (x1 + x2)/(n1 + n2). (a) For a two-tailed test, we may compute +za/2 = ±InvNorm(a/2,0, 1) and check that the test-statistic falls in a tail. Or we may instead compute P = 2 * normalcdf (|TS|, 0,0, 1) and check that P < a. Suppose our null hypothesis is pi p2, that our sample sizes are ni = 1500 and n2 = 1600, and that we find x1 = 506 and x2 = 692. Assume that N1 and N2 are very large. i. If we use a two-tailed test, what is our alternative hypothesis: pi + p2 ? pi < P2 ? or pi > P2 ? ii. What would we conclude if we rejected the null hypothesis with a two-tailed test? iii. Can we reject the null hypothesis at level of significance a = 0.05, using a two-tailed test? iv. Can we reject the null hypothesis at level of significance a = 0.01, using a two-tailed test?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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