The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 4.504.50 minutes. To make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 3838 randomly selected calls. The mean wait time was calculated to be 5.055.05 minutes. Assuming the population standard deviation is 1.831.83 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 4.504.50 minutes with a 99%99% level of confidence?

Step 2 of 3 :  

Compute the value of the test statistic. Round your answer to two decimal places.

To compute the value of the test statistic, we will use the formula for the **z-test** since the population standard deviation is known:

\[
z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}
\]

Where:
- \(\bar{x}\) is the sample mean (5.05 minutes),
- \(\mu_0\) is the population mean under the null hypothesis (4.50 minutes),
- \(\sigma\) is the population standard deviation (1.83 minutes),
- \(n\) is the sample size (38).

Let's plug in the values:

\[
z = \frac{5.05 - 4.50}{\frac{1.83}{\sqrt{38}}}
\]

Now, calculate the value of the test statistic.

\[
z = \frac{0.55}{\frac{1.83}{\sqrt{38}}} = \frac{0.55}{\frac{1.83}{6.1644}} = \frac{0.55}{0.2968} \approx 1.85
\]

So, the value of the test statistic is approximately **1.85**.

Would you like to proceed with the interpretation of this result, or do you have any other questions?

Here are some related questions to consider:
1. What is the next step in hypothesis testing after calculating the test statistic?
2. How do you determine the p-value corresponding to this test statistic?
3. What is the critical z-value for a one-tailed test at the 99% confidence level?
4. How does the test statistic compare to the critical value?
5. What conclusion can you draw from the test statistic?

**Tip:** Always ensure to round the final test statistic to the appropriate number of decimal places as specified in the problem to avoid rounding errors in your conclusion.

Understand hypothesis testing using the Z-test to determine if the mean wait time for customer service calls exceeds a specified requirement. Example calculation with step-by-step solution provided.

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