Question

Because of the complex nature of the U.S. income tax Internal thes Service (IRS). Yet an article published the Detroit Free Press titled “Assistance: IRS Hel 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 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.

Answer 1

Solution:

a. The null and alternative hypotheses are:

b. Under the null hypothesis, the test statistic is:

Where:

Now we can find the p-value as:

Conclusion: Since the p-value is less than the significance level 0.05, we, therefore, reject the null hypothesis and conclude that the accuracy rate is different than 0.69.