Homework7key[1]

5 72 89 92 98 66 97 83 141 70 126 83 112 cylinder

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Unformatted text preview: .5 7.2 8.9 9.2 9.8 6.6 9.7 8.3 14.1 7.0 12.6 8.3 11.2 cylinder strength (Y, 2) 6.1 7.8 5.8 8.1 7.8 7.4 is an unbiased estimator of μ1 – μ2. a) Use the rules of expected value to show that Calculate the estimate for the given data. We want to show that E( ) = μ 1 – μ2 θ = E( ) = E( ) - E( ) (from 5.8) = μ1 – μ2 (because E( ) = E(X) and E( ) = E(Y) and E(X) and E(Y) are unbiased) Therefore, = so = 8.141 – 8.585 = -0.434 = b) Use rules of variance from Chapter 5 to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a), and then compute the estimated standard error. Since X and Y are independent, and are independent so 3 c) Calculate a point estimate of the ratio σ1/σ2 of the two standard deviations. d) Suppose a single beam and a single cylinder are randomly selected. Calculate a point estimate of the variance of the difference X – Y between beam strength and cylinder strength. Since X and Y are independent, 4...
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