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(2 points) Two independent samples have been selected, 83 observations from popu

ID: 3066888 • Letter: #

Question

(2 points) Two independent samples have been selected, 83 observations from population 1 and 82 observations from population 2. The sample means have been calculated to be 8.7 and 2 7.8. From previous experience with these populations, it is known that the variances are ?-36 and ? -30. (a) Determine the rejection region for the test of H0 : (??-42) 2.06 Use 0.02. (Hint: Pay attention to the right side of the hypotheses.) ? 2 (b) Compute the test statistic. (c) The final conclusion is @ A. We can reject the null hypothesis that (??-?) 2.06 B. There is not sufficient evidence to reject the null hypothesis that (1 2)2.06 (d) Construct a 98 % confidence interval for (11-112

Explanation / Answer

a)

z > 2.0537

b)

s1 = sqrt(36) = 6, s2 = sqrt(30) = 5.477

z = ( x1 -x2) - d / sqrt(s1^2/n1 + s2^2/n2)
= (8.7 - 7.8) - 2.06/ sqrt(6^2/83 + (5.477)^2/82)
= -1.404

c) There is not sufficient evidence to reject the null hypothesis that (mu1 - mu2) < = 2.06

d)

z value at 98% = 2.326

CI = (x1 - x2) +/- z * sqrt(s1^2/n1 + s2^2/n2)
= ( 8.7 - 7.8) +/- 2.326 * sqrt(6^2/83 + (5.477)^2/82)
= (-1.1799 , 2.9799)

-1.1799 <= (mu1 - mu2) < = 2.9799