Question

(1 point) Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples. Sample 1: n1 = 18, X1 = 20, $i = 5. Sample 2: n2 = 30, L2 = 15, S2 = 5. (a) The test statistic is (b) Find the t critical value for a significance level of 0.025 for an alternative hypothesis that the first population has a larger mean (one-sided test). Use the more conservative estimate for the number of degrees of freedom: t* = (c) The conclusion is A. There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean and accept that the first population has a larger mean. B. There is not sufficient evidence to warrant rejection of the claim that the two nonulations have the pamamaan

Answer 1

Given 7,= 18, 7,= 20, S,=5 n2 = 30, 73= 15, S255 a) Test statistic tcal = 2 de nothithe -27df = 20 -15= 3.3541 b) t critical value at 0.025 for one Sided test is 1.96. ie. ttable = 1.96 treal > t table then we have to - Reject Ho.

c) The conclusion is . There is sufficient evidence to warrant rejection of the claims that the two populations have the same mean and accept that the first population has a larger mean. Given n=16, 7=28, s=4.82 ne = 13, 2e = 22.6, Sn=7,34 a) degrees of freedom nitng-2= 16+13–2=27 b) Test statistic - tcal = xide - 28-22.6 Vente 14:62)763.3431 = 2.2826 (). The final conclusion is ttable = 2053 2.771 tcal <ttable then we have to accept Ho. A There is not sufficient evidence to reject the null hypothesis that (e-42) = 0. 13