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Let's break down the problem and compute the test statistic step by step.

The problem involves testing the claim about the standard deviation of customer waiting times at a bank. Here are the key details we need:

- The null hypothesis \( H_0: \sigma \geq 1.4 \) minutes.
- The alternative hypothesis \( H_A: \sigma < 1.4 \) minutes (one-tailed test).
- We have a significance level of \( \alpha = 0.01 \).
- The data provided are the waiting times for customers, from which we'll calculate the sample variance.

### Step-by-Step Process:

1. **Calculate the sample variance**:
   First, we compute the sample mean, then the sample variance using the waiting times in the provided table.

2. **Set up the test**:
   The test statistic for the Chi-Square test on variance is given by:

   \[
   \chi^2 = \frac{(n - 1) s^2}{\sigma_0^2}
   \]

   where:
   - \( n \) is the sample size (the number of customer waiting times),
   - \( s^2 \) is the sample variance,
   - \( \sigma_0^2 \) is the hypothesized population variance (in this case, \( 1.4^2 \)).

3. **Find the critical value and p-value**:
   Use the chi-square distribution to find the critical value at \( \alpha = 0.01 \), and compare the test statistic with this critical value.

Let's start by calculating the sample variance using the provided data. I will extract the relevant numbers from the table and compute these values.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you on how to calculate the test statistic manually? You can also upload the data or perform it in a statistical tool like Excel or Python.

Let me know if you have questions or if you'd like further details. Here's a list of related questions:

1. How do you calculate sample variance and standard deviation from data?
2. What are the steps for performing a Chi-Square test for variance?
3. How do you determine the critical value in a Chi-Square test?
4. How do you compute p-values in hypothesis testing?
5. What are the assumptions for using a Chi-Square test for variance?

**Tip**: Always verify that your data is normally distributed when applying tests for variance like the Chi-Square test.

Test the claim that the standard deviation of customer waiting times at a bank is less than 1.4 minutes using a chi-square test. Learn how to calculate the test statistic, sample variance, and determine the p-value. A step-by-step guide suitable for college-level statistics.

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