Problem 2 A supermarket chain has stores in 32 cities. A company official wants to estimate the proportion of stores in the chain that do not meet a specified cleanliness criterion. Stores within each city appear to possess similar characteristics; therefore, she decides to select a two-stage cluster sample containing one-half of the stores within each of four cities. Cluster sampling is desirable in this situation because of travel costs. The data collected are given in the following table. City Number of stores in city Number of stores sampled Number of stores not meeting criterion 0 0 1 25 13 3 2 10 5 3 18 9 4 16 8 1 4 2 (A). Estimate the proportion of stores not meeting the cleanliness criterion and place a bound on the error of estimation. (B). It is given that the chain contains 450 stores. Estimate the proportion of stores not meeting the cleanliness criterion and place a bound on the error of estimation.