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 estimates of the proportions of such claims from each stratum based on our sample.With our simple random sampling of claims from each stratum, we have unbiased estimates of the corresponding population proportion for each stratum. Therefore, if we take the sample proportions 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 stratum had been audited.

(b) (Optional) Give margins of error for your estimates. Hint:

You first need to find standard errors for your sample estimates;

see Chapter 8, page 460. Then you need to use the rules for variances given in Chapter 4 (page 253) to find the standard errors for the population estimates. Finally, you need to multiply by z∗

to determine the margins of error.