255_Ch_7_PracticeProbs_Solns.pdf

255_Ch_7_PracticeProbs_Solns.pdf - 255 Chapter 7 Solutions...

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255 Chapter 7 Solutions 7.1 1 . a. We use the sample mean to estimate the population mean μ . ˆ μ = 113 . 73 b. We use the sample median to estimate the population median. Sample median is 113. c. We use the sample standard deviation which is 12.74. d. With “success”=IQ greater than 100, x=# of successes=30 and ˆ p = 30 / 33 e. We use the sample CV, or s/ ¯ x = 113 . 73 / 12 . 74 5 . ˆ θ 1 = N ¯ x = 1703000 , ˆ θ 2 = T - N ¯ d = 1591300 , ˆ θ 3 = T x/ ¯ y ) = 1601438 . 281 9 . a. 2.11 b. 0.119 11 . a. E ( X 1 /n 1 - X 2 /n 2 ) = E ( X 1 ) /n 1 - E ( X 2 ) /n 2 = p 1 - p 2 b. V ( X 1 /n 1 - X 2 /n 2 ) = p 1 q 1 n 1 p 1 q 1 + p 2 q 2 n 2 p 2 q 2 and the standard error is the square root of this c. We will let ˆ p 1 = x 1 /n 1 , ˆ q 1 = 1 - ˆ p 1 and ˆ p 2 = x 2 /n 2 , ˆ q 2 = 1 - ˆ p 2 d. -0.245 e. 0.041 12 . E ( ( n 1 - 1) S 2 1 +( n 2 - 1) S 2 2 n 1 + n 2 - 2 ) = ( n 1 - 1) σ 2 +( n 2 - 1) σ 2 n 1 + n 2 - 2 = σ 2 15 . a. ˆ θ = X 2 i 2 n b. 74.505 19 . a. Let ˆ p = 2 ˆ λ - 0 . 3 . Then the estimate is 0.2 b. E ( ˆ λ ) = λ and this will give us the unbiasedness that we desire. c. ˆ p = 10 7 ( Y n ) - 9 70 7.2 21 . a. MLE is ˆ p = x/n . Estimate is 0.15 b. E p ) = E ( X ) /n = np/n = p c. 0.4437 1
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23 . a. ˆ θ = 1 1 - ¯ X - 2 is the moment estimator. The estimate is 3 b. ˆ θ = - n ln ( X i ) - 1 is the MLE. The estimator is 3.12
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