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HW 7 solutions _1_

# HW 7 solutions _1_ - Homework 7 Solutions 10-44 a 1 The...

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Homework 7 Solutions 10-44 a) 1) The parameter of interest is the mean difference in impurity level, d where d i = Test 1 Test 2. 2) H 0 : 0 d 3) H 1 : d 0 4) = 0.01 5) The test statistic is n s d t d / 0 6) Reject the null hypothesis if t 0 < 7 , 005 . 0 t or t 0 > 7 , 005 . 0 t where 7 , 005 . 0 t = 3.499 7) d 0.2125 s d 0.1727 n 8 48 . 3 8 / 1727 . 0 2125 . 0 0 t 8) Because 3.499 < 3.48 < 3.499 cannot reject the null hypothesis. There is not sufficient evidence that the tests give different mean impurity levels at = 0.01. b) 1) The parameter of interest is the mean difference in impurity level, d where d i = Test 1 Test 2. 2) H 0 : 0 1 . 0 d 3) H 1 : 0 10 . 0 d 4) = 0.05 5) The test statistic is n s d t d / 1 . 0 0 6) Reject the null hypothesis if t 0 < - 7 , 05 . 0 t where 7 , 05 . 0 t = 1.895 7) d 0.2125 s d 0.1727 n 8 8424 . 1 8 / 1727 . 0 1 . 0 2125 . 0 0 t 8) Because -1.895<-1.8424 we fail to reject the null at the 0.05 level of significance. c) β=1 -0.9=0.1 579 . 0 1727 . 0 1 . 0 d N=8 is not an adequate sample size From the chart VII (g) n≈30 10-55 a) 1) The parameters of interest are the time to assemble standard deviations, 1 2 , 2) H 0 : 1 2 2 2 3) H 1 : 1 2 2 2 4) = 0.02 5) The test statistic is

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2 2 2 1 0 s s f 6) Reject the null hypothesis if f 0 < 1 , 1 1 , 2 / 1 2 n n
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