Because of the complex nature of the U.S. income tax system, many people have questions for the Internal Revenue Service (IRS). Yet an article published by the Detroit Free Press titled “Assistance: IRS Help Centers Give the Wrong Information” discusses the propensity of IRS staff employees to give incorrect tax information to taxpayers who call with questions. Then IRS Inspector General Pamela Gardiner told a Senate subcommittee that “the IRS employees at 400 taxpayer assistance centers nationwide encountered 8.5 million taxpayers face-to-face last year. The problem: When inspector general auditors posing as taxpayers asked them to answer tax questions, the answers were right 69% of the time.” Suppose an independent commission was formed to test whether the 0.69 accuracy rate is correct or whether it is actually higher or lower. The commission has randomly selected n = 180 tax returns that were completed by IRS assistance employees and found that 105 of the returns were accurately completed.
a. State the appropriate null and alternative hypotheses.
b. Using an α = 0.05 level, based on the sample data, what conclusion should be reached about the IRS rate of correct tax returns? Discuss your results.