Using the data of Exercise 1 and assuming simple random sampling, (a) give the ratio-to-size estimate of the population total and (b) estimate the variance of that estimator.

Exercise 1Assume that the following are data from cluster sampling with simple random sampling of clusters. There are 10 clusters (primary units) and a total of 100 secondary units in the population. For each of the n = 3 selected clusters, yi is the cluster total for the variable of interest and Mi is cluster size: y₁ = 4, M1 = 5; y₂ = 12, M₂ = 20; y₃ = 7, M₃ = 10. (a) Give an unbiased estimate of the population total. (b) Estimate the variance of that estimator.