The insulin-binding capacity (pmol/mg protein) was measured for four different groups of rats: (1) Nondiabetic, (2) Untreated diabetic, (3) Diabetic treated with a low dose of insulin, (4) Diabetic treated with a high dose of insulin. The accompanying table gives sample sizes and sample standard deviations. Denote the sample size for the ith treatment by n_i and the sample variance by S²_i (i = 1, 2, 3, 4). Assuming that the true variance for each treatment is σ², construct a pooled estimator of σ² that is unbiased, and verify using rules of expected value that it is indeed unbiased. What is your estimate for the following actual data?

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Sample size Sample SD 1 16 .64 Treatment 2 18 .81 3 8 .51 4 12 .35