In many investigations the population is not surveyed in a single step. Rather, it is often convenient to carry out an initial pilot study in which a relatively small proportion of the sample members are contacted. The results obtained are then analyzed prior to conducting the bulk of the survey. The chief disadvantage of such a procedure is that it can be quite time consuming. However, this factor may be outweighed by several advantages. One important benefit is that the investigator is able, at modest cost, to try out the proposed questionnaire in order to ensure that the various questions can be thoroughly understood, The pilot study may also suggest additional questions whose potential importance had previously been overlooked. Moreover, this study should also provide an estimate of the likely tate of nonresponse. Should this prove unacceptably high, some modification in the method of soliciting responses might appear desirable. Additional Topics in Sampling Conducting a survey in two stages, beginning with a pilot study, is known as two- phase sampling. This approach has two further advantages. First, if stratified random sampling is employed, the pilot study can be used to provide estimates of the individual stratum variances. These, in tum, can be employed to estimate the optimum allocation of the sample among the various strata. Second, the results of the pilot study can be used to estimate the number of observations needed to obtain estimators of population param- eters with a specified level of precision. The following examples serve to illustrate these points. Consider a straightforward situation in which a simple random sample is to be used to estimate a population mean. At the outset, relatively little is known about this population, so an initial pilot survey is to be carried out to get some idea of the sample size required u46 Example 17.6 Mean Value of Accounts Receivable (Sample Size) An auditor wishes to estimate the mean value of accounts receivable in a total popula- tion of 1,120 accounts. He wants to produce a 95% confidence interval for the popula- tion mean, extending approximately $4 on each side of the sample mean. To begin, he takes a simple random sample of 100 accounts, finding a sample standard deviation of $30.27. How many more accounts should be sampled