The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 1.9 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.025. Complete parts (a) through (d) below. E Click on the icon to view the data. a. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: 021.9 minutes O B. Ho: =1.9 minutes HA: G=1.9 minutes HA:G<1.9 minutes OC. Ho: G=1.9 minutes O D. Ho: 6<1.9 minutes HA:G<19 minutes H:0=1.9 minutes b. Compute the test statistic. (Round to two decimal places as needed.) c. Find the P-value of the test statistic. The P-value of the test statistic is (Round to three decimal places as needed.) d. Does the use of the single line appear to reduce the variation among waiting times? There v sufficient evidence to conclude that the single line reduced the variation among waiting times because H, is v by the hypothesis test.

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The image displays a table titled "Customer Waiting Times (in minutes)," which contains several rows and columns of numerical data:

```
8.2  |  7.6  |  6.7  |  6.8
7.3  |  6.6  |  6.1  |  6.4
7.1  |  6.4  |  7.5  |  7.5
6.2  |  7.9  |  8.3  |  7.3
7.3  |  8.9  |  5.4  |  9.4
7.2  |  7.6  |  6.2  |  7.2
7.6  |  6.5  |  7.4  |  7.5
6.4  |  7.2  |  7.8  |  7.0
8.2  |  8.9  |  6.8  |  8.8
6.4  |  7.9  |  7.8  |  7.9
6.5  |  7.4  |  7.4  |  6.4
8.5  |  6.4  |  8.8  |  7.3
11.7 |  6.6  |  7.8  |  6.1
7.6  |  7.2  |  7.5  |  7.8
6.4  |  7.5  |  6.7  |  6.8
```

This table organizes waiting times for customers measured in minutes across different scenarios or instances. Each row represents a set of waiting times under specific circumstances. Analyzing this data can reveal patterns or insights into customer service efficiency.
Transcribed Image Text:The image displays a table titled "Customer Waiting Times (in minutes)," which contains several rows and columns of numerical data: ``` 8.2 | 7.6 | 6.7 | 6.8 7.3 | 6.6 | 6.1 | 6.4 7.1 | 6.4 | 7.5 | 7.5 6.2 | 7.9 | 8.3 | 7.3 7.3 | 8.9 | 5.4 | 9.4 7.2 | 7.6 | 6.2 | 7.2 7.6 | 6.5 | 7.4 | 7.5 6.4 | 7.2 | 7.8 | 7.0 8.2 | 8.9 | 6.8 | 8.8 6.4 | 7.9 | 7.8 | 7.9 6.5 | 7.4 | 7.4 | 6.4 8.5 | 6.4 | 8.8 | 7.3 11.7 | 6.6 | 7.8 | 6.1 7.6 | 7.2 | 7.5 | 7.8 6.4 | 7.5 | 6.7 | 6.8 ``` This table organizes waiting times for customers measured in minutes across different scenarios or instances. Each row represents a set of waiting times under specific circumstances. Analyzing this data can reveal patterns or insights into customer service efficiency.
The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 1.9 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.025. Complete parts (a) through (d) below.

### a. Identify the null and alternative hypotheses. Choose the correct answer below.

- ○ A. \( H_0: \sigma = 1.9 \) minutes   
\( H_a: \sigma < 1.9 \) minutes 

- ○ B. \( H_0: \sigma = 1.9 \) minutes   
\( H_a: \sigma > 1.9 \) minutes 

- ○ C. \( H_0: \sigma \neq 1.9 \) minutes   
\( H_a: \sigma = 1.9 \) minutes 

- ○ D. \( H_0: \sigma < 1.9 \) minutes   
\( H_a: \sigma = 1.9 \) minutes 

### b. Compute the test statistic.

\( \chi^2 = \) \_\_\_\_\_  
(Round to two decimal places as needed.)

### c. Find the P-value of the test statistic.

The P-value of the test statistic is \_\_\_\_\_ .  
(Round to three decimal places as needed.)

### d. Does the use of the single line appear to reduce the variation among waiting times?

There \_\_\_\_ sufficient evidence to conclude that the single line reduced the variation among waiting times because \( H_0 \) is \_\_\_\_ by the hypothesis test.

Note: The text describes a hypothesis testing scenario involving the standard deviation of waiting times at a bank. The goal is to determine if a single line reduces variation compared to multiple lines.
Transcribed Image Text:The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 1.9 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.025. Complete parts (a) through (d) below. ### a. Identify the null and alternative hypotheses. Choose the correct answer below. - ○ A. \( H_0: \sigma = 1.9 \) minutes \( H_a: \sigma < 1.9 \) minutes - ○ B. \( H_0: \sigma = 1.9 \) minutes \( H_a: \sigma > 1.9 \) minutes - ○ C. \( H_0: \sigma \neq 1.9 \) minutes \( H_a: \sigma = 1.9 \) minutes - ○ D. \( H_0: \sigma < 1.9 \) minutes \( H_a: \sigma = 1.9 \) minutes ### b. Compute the test statistic. \( \chi^2 = \) \_\_\_\_\_ (Round to two decimal places as needed.) ### c. Find the P-value of the test statistic. The P-value of the test statistic is \_\_\_\_\_ . (Round to three decimal places as needed.) ### d. Does the use of the single line appear to reduce the variation among waiting times? There \_\_\_\_ sufficient evidence to conclude that the single line reduced the variation among waiting times because \( H_0 \) is \_\_\_\_ by the hypothesis test. Note: The text describes a hypothesis testing scenario involving the standard deviation of waiting times at a bank. The goal is to determine if a single line reduces variation compared to multiple lines.
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