According to the IRS, taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 50 callers who placed their calls to the IRS in the first 30 minutes that the line is open during the day have a mean waiting time of 11 minutes before an IRS telephone assister answers. Based on data from past years, you can assume that the standard deviation of waiting times is 8 minutes. Using these sample results, can you conclude that the waiting time for calls placed during the first 30 minutes the IRS help line is open each day is significantly less that the overall mean waiting time of 13 minutes? Use alpha=0.05

- Establish the two hypotheses
- Calculate the test statistic
- Make a decision using the critical value approach
- Make a decision using the p-value approach

Question

09-12-2022
Mathematics

Answered

According to the IRS, taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 50 callers who placed their calls to the IRS in the first 30 minutes that the line is open during the day have a mean waiting time of 11 minutes before an IRS telephone assister answers. Based on data from past years, you can assume that the standard deviation of waiting times is 8 minutes. Using these sample results, can you conclude that the waiting time for calls placed during the first 30 minutes the IRS help line is open each day is significantly less that the overall mean waiting time of 13 minutes? Use alpha=0.05

- Establish the two hypotheses
- Calculate the test statistic
- Make a decision using the critical value approach
- Make a decision using the p-value approach

Answer :

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qwterabite qwterabite · Answer 1 · 2022-12-21T01:19:29-05:00

We can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.

Two-Hypotheses:

H0: The mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is not significantly less than the overall mean waiting time of 13 minutes.

Ha: The mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.

Test Statistic: t = (11 - 13) / (8/√50) = -2.5 and the Critical Value Approach is: The critical value for a one-tailed test at alpha = 0.05 is 1.645. Since the test statistic (-2.5) is less than the critical value (1.645), we can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes, and the P-Value Approach: The p-value for the one-tailed test is 0.0062. Since this p-value is less than alpha = 0.05, we can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.

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