Statistics Homework Solutions 174

Statistics Homework Solutions 174 - 174 CHAPTER 7 0 478535....

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Unformatted text preview: 174 CHAPTER 7 0 478535. There are 23 degrees of freedom. t23 2 807. 2 807 0 478535 , or (8.063, 10.749). ¨ ¤ ¨ ¥ ¡ ¤ ¢ ¢ ¡ Therefore a 99% prediction interval is 9 4060955 005 ¥ ¡ 2 ¨ x ¡ xi 2 1 x ¡ ∑n i x ¨ 1 n ¤ 1 ¡ s ¥ spred ¨ (h) The confidence interval is more useful, since it is concerned with the true length of the spring, while the prediction interval is concerned with the next measurement of the length. 3. (a) The slope is 0.84451; the intercept is 44.534. (b) Yes, the P-value for the slope is 0 920. ¨ ¡ ¨ ¨ ¢ ¡ ¤ 123 is large, use the z table to construct a confidence interval. 1 645 2 23 , or (74.6, 82.0). ¨ ¤ ¨ ¤ ¡ 1 645, so a 90% confidence interval is 78 31 ¥ ¨ ¡ ¨ ¨ ¡ z 05 ¤ (e) Since n 0 847 ¡¥ r2 52 979 mg/s. ¨ (d) r 0 84451 10 (c) 44 534 0, so horsepower is related to NO x . (f) No. A reasonable range of predicted values is given by the 95% prediction interval, which is (29.37, 127.26). βE 0 ¡ 5. (a) H0 : βC ¡ ¡ ¡ (b) βC and βE are independent and normally distributed with means βC and βE , respectively, and estimated standard deviations sβ 0 03267 and sβ 0 02912. ¢ ¡ ¢ ¨ E ¨ ¡ C Since n 123 is large, the estimated standard deviations can be treated as good approximations to the true standard deviations. ¡ ¡ ¡ 0 032672 0 029122 ¢ ¢ ¢ £¥ ¡ ¡ ¨ ¡ ¤ ¡ ¡ ¡ 0 0358. ¨ ¡ ¨ ¨ ¢ ¨ ¡ ¡ We can conclude that the effect of horsepower differs in the two cases. ¤ 1 ¨ ¡ ¥ ¤ ¡ ¨ ¡ ¡ β1 x ¡ ¡ ¡ ¨ ¡ ¡¥ ¡ ¡ ¡ y 73 266181. ¨ ¨ 0 496785 and β0 yi ¡ ¡ ¥ ¨ ¤¥ ¡ ¡ x yi y 1 xi ∑ n 1 xi x 2 i 1036 888889, ∑n i y ¥ ¤ ¦¥ ¡ ¥ ¤ ¡ ¡ ¤ ∑n i 2 2 ¡ ¡ ¤ ¡ ¡ β1 62 888889, ∑n 1 xi x i 515 111111, n 9. 524 888889, ¨ 7. (a) x 20 888889, y ∑ n 1 xi x y i y i 2 10. 0, the P-value is the sum of the areas to the right of ¡ ¡ 0 0179 0 75269 ¤ 0 0179 ¨ Thus P βE ¡ ¡ Since the alternate hypothesis is of the form βC z 2 10 and to the left of z 2 10. 0 84451 ¨ βE £ ¤ ¥ s2 ¨ βC ¢ s2 ¨ βE ¡ βC ¨ ¡ ¨ The test statistic is z 0 75269. ¡ 0 84451 and βE ¨ βC ...
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This note was uploaded on 12/20/2011 for the course STA 3163 taught by Professor Mattgilg during the Fall '11 term at UNF.

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