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as093-soln

# as093-soln - STAT 854/454 Short Solutions ro Assignment 3 1...

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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 single-stage cluster sampling, estimate the error rate for all 828 claims. Give a standard error for your estimate. Soln: This is one-stage 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 } = 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 . (b) Estimate (with standard error) the total number of errors in the 828 claims.

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as093-soln - STAT 854/454 Short Solutions ro Assignment 3 1...

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