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 entitled "Assistance: IRS Help Centers Give the Wrong Information" discusses the propensity of IRS staff employees to give incorrect tax information to tax-payers 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. State the appropriate null and alternative hypotheses.
A) H0 : p = 0.69 Ha : p ≠ 0.69
B) H0 : p = 0.58 Ha : p ≠ 0.58
C) H0 : p 0.69 Ha : p ≤ 0.69
D) H0 : p 0.58 Ha : p ≤ 0.58

Question

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 entitled "Assistance: IRS Help Centers Give the Wrong Information" discusses the propensity of IRS staff employees to give incorrect tax information to tax-payers 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. State the appropriate null and alternative hypotheses.
A) H0 : p = 0.69 Ha : p ≠ 0.69
B) H0 : p = 0.58 Ha : p ≠ 0.58
C) H0 : p > 0.69 Ha : p ≤ 0.69
D) H0 : p > 0.58 Ha : p ≤ 0.58

Quizplus · Accepted Answer

The null hypothesis (H0) is a statement of no effect or no difference and is tested against the alternative hypothesis (Ha), which suggests a difference. In this case, the null hypothesis is that the accuracy rate (p) is equal to 0.69, as initially reported by the IRS Inspector General. The alternative hypothesis is that the accuracy rate is not equal to 0.69, indicating it could be either higher or lower. This is a two-tailed test because the alternative hypothesis includes possibilities on both sides of the specified value (0.69).

Because of the Complex Nature of the U