10.74: It has been reported that 80% of tax payers who are audited by the Internal Revenue Service end up paying more money in taxes. Assume that auditors are randomly assigned to cases, and that one of the ways the IRS oversees its auditors is to monitor the percentage of cases that result in the taxpayer paying more taxes. If a sample of 400 cases handled by an individual auditor has 77.0% of those she audited paying more taxes, is there a reason to believe her overall “paying more” percentage might be some value other then 80%? Use the 0.10 level of significance in reaching a conclusion. Determine and interpret the p-value for the test.

Answer:

Given information is If a sample of 400(n) cases handled by an individual auditor has 77%(0.77) of those she audited paying more taxes,

Null Hypothesis: P=0.80

Alternative Hypothesis: P≠ 0.80

THe test statistic is given by