Statistics for Managers Using Microsoft Excel, 5e © 2008 Pearson Prentice-Hall, Inc.Chap 8-1 Determining Sample Size  The required sample size can be found to reach a desired margin of error (e) with a specified level of confidence (1 -  )  The margin of error is also called sampling error  the amount of imprecision in the estimate of the population parameter  the amount added and subtracted to the point estimate to form the confidence interval

Statistics for Managers Using Microsoft Excel, 5e © 2008 Pearson Prentice-Hall, Inc.Chap 8-2 Determining Sample Size  To determine the required sample size for the mean, you must know:  The desired level of confidence (1 -  ), which determines the critical Z value  The acceptable sampling error (margin of error), e  The standard deviation, σ Now solve for n to get

Statistics for Managers Using Microsoft Excel, 5e © 2008 Pearson Prentice-Hall, Inc.Chap 8-3 Determining Sample Size If  = 45, what sample size is needed to estimate the mean within ± 5 with 90% confidence? So the required sample size is n = 220

Class Exercise Statistics for Managers Using Microsoft Excel, 5e © 2008 Pearson Prentice-Hall, Inc.Chap 8-4

Class Exercise Statistics for Managers Using Microsoft Excel, 5e © 2008 Pearson Prentice-Hall, Inc.Chap 8-5

Class Exercise Statistics for Managers Using Microsoft Excel, 5e © 2008 Pearson Prentice-Hall, Inc.Chap 8-6

Statistics for Managers Using Microsoft Excel, 5e © 2008 Pearson Prentice-Hall, Inc.Chap 8-7 Applications in Auditing  Six advantages of statistical sampling in auditing  Sample result is objective and defensible  Based on demonstrable statistical principles  Provides sample size estimation in advance on an objective basis  Provides an estimate of the sampling error

Statistics for Managers Using Microsoft Excel, 5e © 2008 Pearson Prentice-Hall, Inc.Chap 8-8 Applications in Auditing  Can provide more accurate conclusions on the population  Examination of the population can be time consuming and subject to more nonsampling error  Samples can be combined and evaluated by different auditors  Samples are based on scientific approach  Samples can be treated as if they have been done by a single auditor  Objective evaluation of the results is possible  Based on known sampling error