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Question 4 Consider a population with size N. Also, suppose there are two strata with sizes N, and N2. We wish to estimate /1 X /2 where Hi represents the mean of the characteristic Y in the ith stratum. In each stratum, we select (independently) a random sample. These random samples have sample sizes n, and n2 respectively. a) Give a "natural" estimator of My X /2 and verify it is unbiased. [4] b) Calculate an estimate of the variance of the estimator in part (a) by expressing it as a function of means and variances (V1, 72, S, and s2). [8] c) Provide an approximate 95% confidence interval for #1 x H2- [2] Total [72] Enjoy! APR 16