A biologist is interested in comparing the weights of toads in two ponds, one of which is polluted. Let μ1 be the average weight of toads in the polluted pond, and let μ2 be the average weight of toads in the unpolluted pond. Assume the standard deviation σ of the weights of the toads is the same in each pond.
(a) If n1 toads are sampled from the polluted pond and n2 toads are sampled from the unpolluted pond, explain how to get an unbiased estimator of the di?erence µ1- µ2
(b) If the cost of sampling n1 toads from the polluted pond and n2 toads from the unpolluted pond is 4n1+n2 and the total cost must be at most 300, what sample sizes n1 and n2 will minimize the variance of the estimator that you found in part (a)?