Question

You may need to use the appropriate appendix table or technology to answer this question The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posted answers to frequently asked questions on its website.t According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of 12 minutes before being able to talk to an IRS employee. Suppose you select a sample of 70 callers after the new phone service has been implemented; the sample results show a mean waiting time of 10 minutes before an IRS employee comes on the line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting time is 8 minutes. Using your sample results, can you conclude that the actual mean waiting time turned out to be significantly less than the 12-minute claim made by the taxpayer advocate? Use α-0.05 State the null and alternative hypotheses. Ho: μ < 12 Ha: μ 12 H0: μ > 12 Ha: μ 12 Ho: μ = 12 Ho: μ 12 Ha: μ > 12 Ha: μ < 12 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject Ho- We cannot conclude that the actual mean waiting time is significantly less than the claim of 12 minutes made by the taxpayer advocate. Do not reject Ho. We cannot conclude that the actual mean waiting time is significantly less than the claim of 12 minutes made by the taxpayer advocate. Do not reject Ho- We can conclude that the actual mean waiting time is significantly less than the claim of 12 minutes made by the taxpayer advocate Reject Ho. We can conclude that the actual mean waiting time is significantly less than the claim of 12 minutes made by the taxpayer advocate

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$$\geq$ 12

H_a : $\mu$ < 12

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (10 - 12) / 8 / $\sqrt$ 70

Test statistic = -2.09

P(z < -2.09) = 0.0183

P-value = 0.0183

$\alpha$ = 0.05

P-value < $\alpha$

Reject the null hypothesis .

O Reject Ho We can conclude that the actual mean waiting time is significantly less than the claim of 12 minutes made by the taxpayer advocate.