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Statistics Homework Solutions 213

Statistics Homework Solutions 213 - 213 SECTION 9.3(b The...

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SECTION 9.3 213 (b) The sample means are X 1 1 998, X 2 3 0000, X 3 5 300. The sample sizes are J 1 5, J 2 J 3 3. The up- per 5% point of the Studentized range is q 3 8 05 4 04. The 5% critical value for X 1 X 2 and for X 1 X 3 is 4 04 1 3718 2 1 5 1 3 2 44, and the 5% critical value for X 2 X 3 is 4 04 1 3718 2 1 3 1 3 2 73. Therefore means 1 and 3 differ at the 5% level. 13. (a) X 88 04, I 4, J 5, MSTr I i 1 J X i X 2 I 1 19 554. F MSTr MSE 19 554 3 85 5 08. There are 3 and 16 degrees of freedom, so 0 01 P 0 05 (a computer package gives P 0 012). The null hypothesis of no difference is rejected at the 5% level. (b) q 4 16 05 4 05, so catalysts whose means differ by more than 4 05 3 85 5 3 55 are significantly different at the 5% level. Catalyst 1 and Catalyst 2 both differ significantly from Catalyst 4. 15. The value of the F statistic is F MSTr MSE 19 554 MSE. The upper 5% point of the F 3 16 distribution is 3.24. Therefore the F test will reject at the 5% level if 19 554 MSE 3 24, or, equivalently, if MSE 6 035.
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