finalrevsol

finalrevsol - Solutions to Final Review Problems 1. This is...

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Unformatted text preview: Solutions to Final Review Problems 1. This is a paired data problem. The differenced data (first garage minus second garage) is 2 7 16 32 24- 14 2- 9 This differenced data has mean 7 . 5 and variance 248 . 5714. Test H : μ D = 0 H a : μ D 6 = 0 where μ D is the true mean of the difference population. Test statistic: t = X- μ s/ √ n = 7 . 5- q 248 . 5714 / 8 ≈ 1 . 35 The rejection region, based on α = 0 . 01 and n- 1 = 7 df, is the two-tailed area under the t (7) curve to the right of 3 . 50 and to the left of- 3 . 50. Since our test statistic is not in this rejection region, we fail to reject the null hypothesis in favor of the alternative at 0 . 01 level of significance. That is, there is not significant evidence to suggest that the true mean minor repair costs differ for the two garages. 2. This is a two sample Z-test. The mean difference is: 3975 .- 2795 . 0 = 1180 . (Maybe you decided to go the other way and you got- 1180. This is okay too.) The variance of the difference is: s 2 1 n 1 + s 2 2 n 2 = 245 . 1 2 40 + 293 . 7 2 40 = 3658 . 342 The Z critical value for a two-sided 99% confidence interval is 2 . 575. The answer is then 1180 ± (2 . 575) √ 3658 . 342 (1024 . 253 , 1335 . 747) Since this interval does not contain zero, it provides evidence that the true average durability index differs for the two fabrics. 3. This is another paired t-test. The differenced data (before minus after) is 2 8- 3 7 12 This differenced data has mean 5 . 2 and variance 33 . 7. Test H : μ D = 0 H a : μ D > where μ D is the true mean of the differenced population “before minus after”....
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This note was uploaded on 01/23/2011 for the course APPM 5440 at Colorado.

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finalrevsol - Solutions to Final Review Problems 1. This is...

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