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Hw8Sol

# Hw8Sol - Homework Solutions Assignment Number 8 Due Section...

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Homework Solutions Assignment Number 8 Due March 12, 2007 Section 7.4. Problem 25. As n increases, Student t pdfs converge to the standard normal pdf, f Z ( z ). (See problem 7.3.13) Section 7.5. Problem 3. (a) 2.088 (b) 7.261 (c) 14.041 (d) 17.539 Problem 5. χ 2 . 95 , 200 . = 200 1 - 2 9(200) + 1 . 64 s 2 9(200) ! 3 = 233 . 9 . Problem 8 G . If n = 19 and σ 2 = 12 . 0, 18 S 2 12 . 0 has a χ 2 distribution with 18 df, so . 95 = 1 - . 05 = P ( χ 2 . 05 / 2 , 18 χ 2 18 χ 2 1 - . 05 / 2 , 18 ) = P 8 . 231 18 S 2 12 . 0 31 . 526 = P (5 . 49 S 2 21 . 02). Problem 15 G . Test H 0 : σ 2 = 1 versus H 1 : σ 2 > 1. The sample variance is 30(19195 . 7938) - (758 . 62) 2 30(29) = 0 . 425 The test statistic is χ 2 = 29(0 . 425) 1 = 12 . 325 . The critical value is χ 2 . 95 , 29 = 42 . 557. Since 12 . 325 < 42 . 557, we accept the null hypothesis and assume the machine is working properly.

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