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A retail store with four departments has charge accounts arranged by department, with pastdue accounts at the top of each departmental list. Suppose the departments average around ten accounts each? with approximately 4D% past due. On a given day the accounts might appear as shovm in the accompanying table {with account numbers 1 through 4D}. The store wishes to estimate the proportion of pastdue accounts by systematic sampling. Department Account number 1 11 12 2D 2128 2940 Delinquent accounts 1y2y3yr;l 12? 13?14 21y22y23y24125 2913013132 a. List all possible 1in1D systematic samples and compute the exact variance of the sample proportion. [Note that there are ten possible values? not all distinct? for the sample proportion? each with probability 1 I ll] of occurring.) b. List all 1in5 systematic samples and compute the exact variance of the sample proportion. c. Compare the result in part a with an approximate variance obtained in a simple random sample of size n. = 4 from this population. Similarly} compare the result in part b with that obtained from a simple random sample with n. = 8. What general conclusions can you make