5. To test the null hypothesis that two population means satisfy µi = P2 by using two independent samples of sizes ni and n2, we require that ni > 30, that n2 > 30, that ni < N1/20 and that n2 < N2/20. Our test statistic TS is V + where 71 and F2 are the sample means, and s1 and s2 are the sample standard deviations. For the degrees of freedom, we take the smaller of ni – 1 and n2 – 1. (b) For a right-tailed test, we may compute to = -InvT(a, dof) and check that the test-statistic falls in the tail. Or we may instead compute P = tcdf (|TS,00, dof), then check that P< a and TS > 0. Suppose our null hypothesis is the population means agree (u1 = µ2), that n1 = 153, 71 = 36.15, and s = 9.67; and that n2 197, F2 = 34.02, and s2 8.90. i. If we use a right-tailed test, what is our alternative hypothesis: H1 # 42? µi < µ2 ? or u1 > 42 ? ii. What would we conclude if we rejected the null hypothesis with a right-tailed test? iii. Can we reject the null hypothesis at level of significance a = 0.05, using a right-tailed test?
5. To test the null hypothesis that two population means satisfy µi = P2 by using two independent samples of sizes ni and n2, we require that ni > 30, that n2 > 30, that ni < N1/20 and that n2 < N2/20. Our test statistic TS is V + where 71 and F2 are the sample means, and s1 and s2 are the sample standard deviations. For the degrees of freedom, we take the smaller of ni – 1 and n2 – 1. (b) For a right-tailed test, we may compute to = -InvT(a, dof) and check that the test-statistic falls in the tail. Or we may instead compute P = tcdf (|TS,00, dof), then check that P< a and TS > 0. Suppose our null hypothesis is the population means agree (u1 = µ2), that n1 = 153, 71 = 36.15, and s = 9.67; and that n2 197, F2 = 34.02, and s2 8.90. i. If we use a right-tailed test, what is our alternative hypothesis: H1 # 42? µi < µ2 ? or u1 > 42 ? ii. What would we conclude if we rejected the null hypothesis with a right-tailed test? iii. Can we reject the null hypothesis at level of significance a = 0.05, using a right-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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Solve questions 1 through 4 please
Transcribed Image Text:5. To test the null hypothesis that two population means satisfy Hi = µ2 by using two independent samples of
sizes ni and n2, we require that ni > 30, that n2 > 30, that ni < N1/20 and that n2 < N2/20. Our test
statistic TS is
I1 – T2
+
where 71 and Iz are the sample means, and sı and s2 are the sample standard deviations. For the degrees of
freedom, we take the smaller of n1 – 1 and n2 – 1.
(b) For a right-tailed test, we may compute ta = -InvT(a, dof) and check that the test-statistic falls in the
tail. Or we may instead compute P = tcdf(|TS|, 0, dof), then check that P < a and TS > 0. Suppose
our null hypothesis is the population means agree (µ1 = µ2), that n1 = 153, 71 = 36.15, and s1 = 9.67;
and that n2 = 197, F2 = 34.02, and s2 = 8.90.
i. If we use a right-tailed test, what is our alternative hypothesis: µ1 # 42 ? µ1 < µ2 ? or µi > µ2 ?
ii. What would we conclude if we rejected the null hypothesis with a right-tailed test?
iii. Can we reject the null hypothesis at level of significance a = 0.05, using a right-tailed test?
iv. Can we reject the null hypothesis at level of significance a = 0.01, using a right-tailed test?
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