4 The article from which the data in Exercise I was extracted also gave the accompanying strength observations for cylinders 6 1

Question

4 The article from which the data in Exercise I was extracted also gave the accompanying strength observations for cylinders 6 1 5 8 7 8 7 1 7 2 9 2 6 6 8 3 7 0 8 3 7 8 8 1 7 4 8 5 8 9 9 8 9 7 14 1 12 6 11 2 Prior to obtaining data denote the beam strengths by X X and the cylinder strengths by Y Y Suppose that the X s constitute a random sample from a distribution with mean and standard deviation o and that the Y s form a random sample independent of the X s from another distribution with mean and standard deviation a Use rules of expected value to show that X Y is an unbiased estimator of H Calculate the esti mate for the given data 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 c Calculate a point estimate of the ratio o o of the two standard deviations d Suppose a single beam and a single cylinder are ran domly selected Calculate a point estimate of the vari ance of the difference X Y between beam strength and cylinder strength

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