9.46 Population estimates. Refer to the previous exercise. One reason to do an audit such as this is to estimate the number of claims that would not be allowed if all claims in a population were examined by experts. We have an estimate of the proportion of unallowed claims from each stratum based on our sample. We know the corresponding population proportion for each stratum. Therefore, if we take the sample proportions of unallowed claims and multiply by the population sizes, we would have the estimates that we need. Here are the population sizes for the three strata:
| Stratum | Claims in strata |
| Small | 3342 |
| Medium | 246 |
| Large | 58 |
(a) For each stratum, estimate the total number of claims that would not be allowed if all claims in the strata had been audited.
(b) Give margins of error for your estimates. ([Hint: you first need to find standard errors for your sample estimates using material presented in Chapter 8 (page 486). Then you need to use the rules for variances from Chapter 4 (page 258) to find the standard errors for the population estimates. Finally, you need to multiply by z* to determine the margins of error.])