It has been reported that 80% of taxpayers who are audited by the IRS end up paying more money in taxes. Assume that the auditors are randomly assigned cases and that one of the ways the IRS oversees its auditors is to monitor the percentage of cases that result in the tax payer paying more in taxes. A sample of 400 cases handles by an individual auditor has 77% or those she audited paying more taxes.
a. Doe the sample data provide evidence to conclude that the auditor's over "pay more" percentage might be some value other than 80%? Use the .10 level of significance in reaching this conclusion. Use the 5-step hypothesis testing procedure.
1. Formulate the null and alternative hypotheses.
2. Determine the criterion for rejection or non-rejection of the null hypothesis.
3. Calculate the test statistic.
4. Compare the test statistic to the rejection region and make a judgment about the null and alternative hypotheses.
5. Interpret the statistical decision in terms of the problem.
6. Compute the observed p-value in the hypothesis test and interpret this value. What does this mean?
Step by step method for computing test statistic Z test for proportion is given in the answer.