# HW10Solutions - Homework 10 Solution 1. Provided that the...

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Homework 10 Solution 1. Provided that the two sample sizes are large, a CI for μ 1 - μ 2 with a conﬁdence level of approximately 1 - α is ¯ x - ¯ y ± z α/ 2 r s 2 1 m + s 2 2 n Plug in the data, we get the following 95% conﬁdence interval, 10 . 4 - 9 . 26 ± 1 . 96 × r 4 . 83 2 97 + 4 . 68 2 148 ,i.e.(-0.08,2.36). 2. (a). Use the paired t test ¯ d ± t α/ 2 ,n - 1 s D / n , we get the following 95% conﬁdence interval, (-2.67,17.17). (b).If we mistakenly thought that these were independent, then we use the 2-sample test ¯ X - ¯ Y - ( μ 1 - μ 2 ) r S 2 1 m + S 2 2 n (-4.09,18.59). (c). The correlation between the U and A samples is P x i y i σ x σ y = 0 . 366. 3. Use F test S 2 1 σ 2 1 S 2 2 2 2 to get the conﬁdence interval of the two variances. P ( F 1 - α/ 2 ,m - 1 ,n - 1 < F < F α/ 2 ,m - 1 ,n - 1 ) = 1 - α , plug in the data, we get the 90% conﬁdence interval for the ratio σ 2 2 2 1 (0.717,15.63), and the CI for the ratio of the two standard deviations is (0.85,3.95).(The CI for σ 2 1 2 2 is(0.064,1.39) and the CI for σ 1 2 is (0.253,1.18)). 4. (a). The picture is on the last page. (b). A ( μ 1 2 1 ), B N ( μ 2 2 2 ). H 0 : σ 2 1 2 2 = 1 , H 1 : σ 2 1 2 2 6 = 1. s 2 1 = (11 . 2735) 2 ,s 2 2 = (11 . 8022) 2 . The test statistic value is: f = s 2 1 s 2 2 = 0 . 9124 We reject H 0 if f F 0 . 05 , 10 , 10 = 2 . 9782 or f F 0 . 95 , 10 , 10 = 0 . 3358 . Since f is not in the rejection region, we fail to reject H 0 and conclude that there is no signiﬁcant diﬀerence between between 2 standard deviations. The 90% CI of σ 2 1 2 2 is given by [ 1 F 0 . 05 , 10 , 10 s 2 1 s 2 2 , 1 F 0 . 95 , 10

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## This note was uploaded on 09/06/2009 for the course ENGRD 2700 taught by Professor Staff during the Spring '05 term at Cornell University (Engineering School).

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HW10Solutions - Homework 10 Solution 1. Provided that the...

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