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 posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). 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  minutes before being able to talk to an IRS employee. Suppose you select a sample of  callers after the new phone service has been implemented; the sample results show a mean waiting time of  minutes before an IRS employee comes on line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting times is  minutes. Use .

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 posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). 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 14 minutes before being able to talk to an IRS employee. Suppose you select a sample of 50 callers after the new phone service has been implemented; the sample results show a mean waiting time of 12 minutes before an IRS employee comes on line. Based upon data from past years, you decide it is reasonable to assume that the standard deviation of waiting times is 10 minutes. Use a = 0.05. a. State the hypotheses. | greater than or equal to 14 - less than 14 b. What is the p-value (to 4 decimals)? c. Using a = 0.05, can you conclude that the actual mean waiting time is significantly less than the claim of 14 minutes made by the taxpayer advocate. No

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 14
Alternative Hypothesis: μ < 14

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (12 - 14)/(10/sqrt(50))
z = -1.41

P-value Approach
P-value = 0.0793
As P-value >= 0.05, fail to reject null hypothesis.