State the null and alternative hypotheses. (Enter != for # as needed.) Ho H₂ 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. O Reject Ho. We cannot conclude that callers who use the IRS help line early in the day have a shorter wait. Reject Ho. We can conclude that callers who use the IRS help line early in the day have a shorter wait. Do not reject Ho. We can conclude that callers who use the IRS help line early in the day have a shorter wait. Do not reject Ho. We cannot conclude that callers who use the IRS help line early in the day have a shorter wait.
State the null and alternative hypotheses. (Enter != for # as needed.) Ho H₂ 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. O Reject Ho. We cannot conclude that callers who use the IRS help line early in the day have a shorter wait. Reject Ho. We can conclude that callers who use the IRS help line early in the day have a shorter wait. Do not reject Ho. We can conclude that callers who use the IRS help line early in the day have a shorter wait. Do not reject Ho. We cannot conclude that callers who use the IRS help line early in the day have a shorter wait.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Hypothesis Testing on IRS Wait Times: An Educational Exercise**
**Scenario:**
Suppose 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 60 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 decide that it is reasonable to 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 than the overall mean waiting time of 13 minutes? Use α = 0.05.
1. **State the null and alternative hypotheses:** (Enter != for ≠ as needed.)
\[
H_0: \mu = 13 \\
H_a: \mu < 13
\]
2. **Find the value of the test statistic:** (Round your answer to two decimal places.)
\[
t = ?
\]
3. **Find the p-value:** (Round your answer to four decimal places.)
\[
p \text{-value} = ?
\]
4. **State your conclusion:**
- \( \square \) **Reject \( H_0 \)**: We cannot conclude that callers who use the IRS help line early in the day have a shorter wait.
- \( \square \) **Reject \( H_0 \)**: We can conclude that callers who use the IRS help line early in the day have a shorter wait.
- \( \square \) **Do not reject \( H_0 \)**: We can conclude that callers who use the IRS help line early in the day have a shorter wait.
- \( \square \) **Do not reject \( H_0 \)**: We cannot conclude that callers who use the IRS help line early in the day have a shorter wait.
**Note:** For these computations, you should refer to relevant statistical tables or software to find the value of the test statistic and the p-value. This information will allow you to determine whether to reject the null hypothesis in favor of the alternative hypothesis.
For further assistance, make sure](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4ed8498-f2f2-4dcb-bcb0-3b3cd025dd21%2F0b33911c-f536-43b0-a899-efdf7761bf91%2Fm2agdhq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing on IRS Wait Times: An Educational Exercise**
**Scenario:**
Suppose 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 60 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 decide that it is reasonable to 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 than the overall mean waiting time of 13 minutes? Use α = 0.05.
1. **State the null and alternative hypotheses:** (Enter != for ≠ as needed.)
\[
H_0: \mu = 13 \\
H_a: \mu < 13
\]
2. **Find the value of the test statistic:** (Round your answer to two decimal places.)
\[
t = ?
\]
3. **Find the p-value:** (Round your answer to four decimal places.)
\[
p \text{-value} = ?
\]
4. **State your conclusion:**
- \( \square \) **Reject \( H_0 \)**: We cannot conclude that callers who use the IRS help line early in the day have a shorter wait.
- \( \square \) **Reject \( H_0 \)**: We can conclude that callers who use the IRS help line early in the day have a shorter wait.
- \( \square \) **Do not reject \( H_0 \)**: We can conclude that callers who use the IRS help line early in the day have a shorter wait.
- \( \square \) **Do not reject \( H_0 \)**: We cannot conclude that callers who use the IRS help line early in the day have a shorter wait.
**Note:** For these computations, you should refer to relevant statistical tables or software to find the value of the test statistic and the p-value. This information will allow you to determine whether to reject the null hypothesis in favor of the alternative hypothesis.
For further assistance, make sure
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