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Unformatted text preview: STAT 854/454 Short Solutions ro Assignment 3 1. An accounting firm is interested in estimating the error rate in a compliance audit it is conducting. The population contains 828 claims, and each claim consists of 215 fields. The firm audits 85 claims selected using SRSWOR, and all 215 fields are checked for errors for each selected claim. It is found that one claim has errors in 4 of the 215 fields, one claim has three errors, 4 claims have two errors, 22 claims have one error, and the remaining 57 claims have no error. (a) Treating this as singlestage cluster sampling, estimate the error rate for all 828 claims. Give a standard error for your estimate. Soln: This is onestage cluster sampling with clusters of equal sizes. N = 828, M i = M = 215, n = 85, and y = 1 M 1 n n X i =1 t i = 1 nM { 1 4 + 1 3 + 4 2 + 22 1 + 57 } = 0 . 002025 . v ( y ) = 1 n N 1 n 1 M 2 1 n 1 n X i =1 ( t i M y ) 2 = 1 . 275 10 7 . The standard error of y is given by q v ( y ) = 3 . 57 10 4 ....
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This note was uploaded on 11/23/2010 for the course STAT 454 taught by Professor Da during the Fall '09 term at Waterloo.
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