The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers

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 15 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 13 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 11 minutes. Using your sample results, can you conclude that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate? Use ? = .05.

a. State the hypotheses.
H0: ? - Select your answer -greater than or equal to 15less than or equal to 15less than 15Item 1
Ha: ? - Select your answer -more than 15greater than or equal to 15less than 15Item 2

b. What is the p-value (to 4 decimals)?

c. Using ? = .05, can you conclude that the actual mean waiting time is significantly less than the claim of 15 minutes made by the taxpayer advocate.
- Select your answer -YesNo

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Explanation / Answer

Solution:-

a)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: ? > 15
Alternative hypothesis: ? < 15

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 1.55563
DF = n - 1

D.F = 49
t = (x - ?) / SE

t = - 1.29

where s is the standard deviation of the sample, x is the sample mean, ? is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of -1.29.

Thus the P-value in this analysis is 0.102.

Interpret results. Since the P-value (0.102) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we cannot conclude that the actual mean waiting time is significantly less than the claim of 15 minutes made by the taxpayer advocate.

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