Question:
A consumer advocacy group is concerned about the ability of tax preparation firms to correctly prepare complex returns. To test the performance of tax preparers in two different tax preparation firms-Quick Tax and Discount Tax-the group designed ten tax cases for families with gross annual incomes between $100,000 and $200,(XX). In a "tax-off" competition, the advocacy group randomly assigned pairs of preparers from the two firms to the ten cases and asked each preparer to compute the tax liability for his or her assigned case. The preparers' returns were collected, and the group computed the difference between each preparer's computed tax and the actual tax that should have been computed. The data below consist of the resulting two sets of tax computation errors, one for preparers from Quick Tax and the other for preparers from Discount Tax. Fully interpret the following MINITAB output of a Wilcoxon signed ranks test analysis of these data.
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Tax Quick Tax Discount Tax Case Errors Errors Difference 156 200 202 390 526 749 911 920 2,145 2,602 701 720 1 857 920 3 1,090 4 1,594 5 1,820 6 1,943 7 1,987 8 2,008 9 2,083 10 2,439 1,204 1,294 1,194 1,076 1,088 -62 - 163 2000 - 1000 O 500 1000- Discount Quick Firm Test of median 0.0 versus median not 0.0 N N for Teat Wilcoxon Statistic P Estimated Median 898.0 Q-D 10 10 52.0 0.014