Let S 1 2 and S 2 2 be the variances of independent random samples of sizes

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Let S12 and S22 be the variances of independent random samples of sizes n1 and n2 selected from normally distributed populations with parameters (μ1, σ2) and (μ2, σ2), respectively. Thus, the populations have different means, but a common variance σ2. To estimate the common variance, we can combine information from both samples and use the pooled estimator

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Use Theorems 6.11 and 6.12 to show that (n1 + n2 - 2)Sp22 has a chi-square distribution with v = (n1 + n2 - 2) degrees of freedom.

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Statistics For Engineering And The Sciences

ISBN: 9781498728850

6th Edition

Authors: William M. Mendenhall, Terry L. Sincich

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