Statistics Homework Solutions 162

Statistics Homework Solutions 162 - 162 CHAPTER 6 2 2 σY...

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Unformatted text preview: 162 CHAPTER 6 2 2 σY ¡ ¢ ¡ 0 3342. ¡ 0 3342 ¡ 0 3342. The null and alternate hypotheses are H0 : µV ¨ ¨ 3 96. 25. ¨ 3 96. ¡ ¡ ¨ ¨ £ ©¥ ¡ ¨ 0. µ0 , the P-value is the area to the right of z ¨ ¡ ¡ ¡ ¤ ¡ Since the alternate hypothesis is of the form µ Thus P ¨ ¨ 25 0 3342 25 versus H1 : µV ¡ ¡ 26 323, σV 26 323 ∂V ∂Y ¡ z σ2 X 26 323, σV V (b) V 2 ¨ ∂V ∂X σV (c) Yes, V is approximately normally distributed. 3. (a) Using Method 1, the limits of the 95% confidence interval are the 2.5 and 97.5 percentiles of the bootstrap means, X 025 and X 975 . Y976 2 £ ¥ ¢ 38 3818, and the 97.5 percentile is Y975 38 53865. ¡ ¤ ¨ ¡ Y26 2 ¨ £ ¥ ¢ The 2.5 percentile is Y25 ¤ The confidence interval is (38.3818, 38.53865). Values outside this interval can be rejected at the 5% level. Therefore null hypotheses (ii) and (iv) can be rejected. (b) Using Method 1, the limits of the 90% confidence interval are the 5th and 95th percentiles of the bootstrap means, X 05 and X 95 . Y951 2 £ ©¥ ¢ 38 39135, and the 95th percentile is Y950 ¡ ¤ ¨ ¡ Y51 2 38 5227. ¨ £ ©¥ ¢ The 5th percentile is Y50 ¤ The confidence interval is (38.39135, 38.5227). Values outside this interval can be rejected at the 10% level. Therefore null hypotheses (i), (ii), and (iv) can be rejected. No, the value 103 is an outlier. 39 833, s2 s2 AB £ ¨ ¡ 200 28, s2 B ¡ ¨ ¡ 7. (a) s2 A 5 02. ¨ 5. (b) No, the F -test requires the assumption that the data are normally distributed. These data contain an outlier (103), so the F -test should not be used. 0 37 ¨ ¡ X s 7 . H0 will be rejected if t 7 ¤£ ¡ (b) The power is approximately 0.60. ¡ 9. (a) The test statistic is t 2 447. ¨ (c) P ...
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