106. 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 ni and the sample variance by (i  1, 2, 3, 4). Assuming that the true variance for each treatment is s2, construct a pooled estimator of s2 that is unbiased, and verify using rules of expected value that it is indeed unbiased. What is your estimate for the following actual data? (Hint: Modify the pooled estimator from Section 10.2.) S2p S2i Treatment 1 2 3 4 Sample size 16 18 8 12 Sample SD .64 .81 .51 .35