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 1 of 3 :

State the null and alternative hypotheses for the test. Fill in the blank below.

To determine whether the mean wait time for customers is longer than the required 4.50 minutes, we need to formulate the null and alternative hypotheses. These hypotheses will help us assess whether there is sufficient evidence to support the claim that the mean wait time exceeds 4.50 minutes.

**Step 1: State the null and alternative hypotheses.**

- **Null Hypothesis (H₀):** The mean wait time is at most 4.50 minutes.
  
  \( H_0: \mu \leq 4.50 \)

- **Alternative Hypothesis (H₁):** The mean wait time is longer than 4.50 minutes.

  \( H_1: \mu > 4.50 \)

These hypotheses set the stage for a one-tailed test to determine if the mean wait time exceeds the required threshold.

Do you want details on how to proceed with the test, or do you have any other questions?

Here are some related questions to consider:
1. What type of statistical test would be appropriate for this hypothesis?
2. How do you calculate the test statistic for this scenario?
3. What is the critical value for a 99% confidence level in a one-tailed test?
4. How do you interpret the results of this hypothesis test?
5. What are the potential consequences of Type I and Type II errors in this context?

**Tip:** When formulating hypotheses, always align the null hypothesis with the status quo or a statement of no effect, and the alternative hypothesis with the claim or the effect you want to test.

Explore hypothesis testing to determine if the mean wait time for customer service calls exceeds 4.50 minutes. Learn how to apply statistical tests with a population standard deviation of 1.83 minutes and a sample size of 38 calls.

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