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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 ( 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 12 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 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 = .05.

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 9.3, Problem 19E
Textbook Problem
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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 (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 12 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 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 = .05.

To determine

Test whether the actual mean waiting time turned out to be significantly less than the 12-minute claim made by the taxpayer advocate.

Explanation of Solution

Calculation:

The given information is that the sample size is n=50, the sample mean is x¯=10 and the population standard deviation is σ=8.

Here, the claim is that the actual mean waiting time turned out to be significantly less than the 12-minute claim made by the taxpayer advocate. This can be written as μ<12. The complement of the claim is, μ12. In the given experiment, the alternative hypothesis indicates the claim.

The null and alternative hypotheses are,

Null hypothesis:

H0:μ12

Alternative hypothesis:

Ha:μ<12 (claim)

Test statistic and p-value:

Software Procedure:

Step-by-step procedure to obtain the test statistic using the MINITAB software:

  • Choose Stat > Basic Statistics > 1-Sample Z.
  • In Summarized data, enter the sample size as 50 and mean as 10

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Chapter 9 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT
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