Example 9.3 Estimating Total Tax Refunds Confidence Interval for a Total.

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Presentation transcript:

Example 9.3 Estimating Total Tax Refunds Confidence Interval for a Total

| 9.2 | 9.4 | 9.5 | 9.6 | 9.7 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | Objective To use StatPro’s one-sample procedure, with an appropriate modification, to find a 95% confidence interval for the total (net) amount the IRS must pay out to these 10,000 taxpayers.

| 9.2 | 9.4 | 9.5 | 9.6 | 9.7 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | Background Information n Suppose the Internal Revenue Service would like to estimate the total net amount of refund due to a particular set of 10,000 taxpayers. n Each taxpayer will either receive a refund, in which case the net refund is positive, or will have to pay an amount due, in which case the net refund is negative. n Therefore the total net amount of refund is a natural quantity of interest; it is the net amount that the IRS will have to pay out (or receive, if negative).

| 9.2 | 9.4 | 9.5 | 9.6 | 9.7 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | IRS.XLS n This file contains data from a random sample of 500 taxpayers. n We need to find a 95% confidence interval for this total using the refund data given.

| 9.2 | 9.4 | 9.5 | 9.6 | 9.7 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | Solution n There is no explicit StatPro procedure for dealing with population totals; however, we can take advantage of the close relationship between the confidence interval for a mean and the confidence interval for a total. n We first use StatPro to find a 95% confidence level for the population mean. n The average refund per taxpayer is slightly less than $300 and the standard error of this sample mean is about $26. The confidence interval for the mean extends from $244 to $346. This is for a single taxpayer.

| 9.2 | 9.4 | 9.5 | 9.6 | 9.7 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | Solution -- continued

| 9.2 | 9.4 | 9.5 | 9.6 | 9.7 | 9.8 | 9.9 | 9.10 | 9.11 | 9.12 | 9.13 | 9.14 | Solution -- continued n Now all we need to do is project these results to the entire population. n To do this we multiply each of these values by the population size, 10,000. n The IRS can be 95% confident that it will need to pay out somewhere between 2.44 and 3.46 million dollars to these 10,000 taxpayers.