Question

(2 points) Ten randomly selected people took an IQ test A, and next day they took a very similar IQ test B. Their scores are shown in the table below. Person A B C D E F G H Test A 94 130 71 119 91 101 85 96 112 107 Test B 96 130 69 121 93 104 84 100 111 105 1. Consider (Test A - Test B). Use a 0.05 significance level to test the claim that people do better on the second test than they do on the first. (Note: You may wish to use software.) (a) What test method should be used? A. Matched Pairs B. Two Samplet C. Two Sample z (b) The test statistic is (c) The critical value is (d) Is there sufficient evidence to support the claim that people do better on the second test? A. Yes B. No 2. Construct a 95% confidence interval for the mean of the differences. Again, use (Test A - Test B). <u

Answer 1

Given that n=10 de 0:05, Since - p. same p. set of people for test A and test B goe then their scores are not independent but paired then en e dore me use Matched paire t.test. option (0 is correct. Ho. There Nell hypothesis. is no difference between both test is mean scores. Hoid=o. or Ho M, - M2=0. Alternative hypothesis His people do better on the second test than they do on the first. Hi Mi < 42. or Mr. ako. test statistic firstly we calculate seam of difference and standard deviation of difference Total 119 91 Person A B с TestA 94 130 1 Test B. 96 130 69 -2 O 2 d² 4 4 D E F G H 1 J 101 85 96 112 102 121 93 104 84 loo 111 105 -2 -2 -3 -4. 2 9 16 4 1 - 4 4 :-7 47. - - . T= -7 -0.7 lo standard deviation se J ted? = to [47-99 tech 2.163, 10-1

test statistic t = व s/n 0,7 2:163/VTO t = -1.023 (ъ at df = n = 9 2 20.05 The critical value is - -1,833 Since Critical tvalue Leadcalated it value » Fail to refeat Ho There is not sufficient evidence to support the claim that people do better on the second test, -2 1 95% confidence interval for difference. t value at 2=0.05, df=9= 2.262 CI = a & talno s van -017 h 2,26 2x 0,684 = -0.1 + 1,5472 e I - ( - 2.2472, 0.8472).