You manage two call centers and are working on trying to reduce the amount of time customers are placed on hold. You believe the mean hold times at the two call centers are not the same so you start by testing the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2. You wish to test the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2 at a significance level of a = 0.002. You obtain the following two samples of data from each center. Each data point is the amount of time (in seconds), a customer is placed on hold. Call Center 1 Call Center 2 103.8 79.1 73.0 84.8 87.0 86.8 64.1 84.2 65.2 62.1 94.7 81.3 80.6 79.1 118.6 48.7 94.7 60.6 77.7 83.0 73.0 47.8 94.2 112.4 51.9 77.1 111.1 a. What is the test statistic for this sample? test statistic = Round to 4 decimal places. b. What is the p-value for this sample? p-value = Round to 4 decimal places. c. The p-value is.. O less than (or equal to) a O greater than a

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### Hypothesis Testing: Interpreting Results

#### d. Decision Based on Test Statistic

After calculating the test statistic, you need to decide whether to:
- **Reject the null hypothesis**
- **Accept the null hypothesis**
- **Fail to reject the null hypothesis**

#### e. Concluding the Hypothesis Test

Your conclusion from the hypothesis test could be one of the following:

- **There is sufficient evidence to warrant rejection of the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.**
- **There is not sufficient evidence to warrant rejection of the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.**
- **The sample data support the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.**
- **There is not sufficient sample evidence to support the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.**
Transcribed Image Text:### Hypothesis Testing: Interpreting Results #### d. Decision Based on Test Statistic After calculating the test statistic, you need to decide whether to: - **Reject the null hypothesis** - **Accept the null hypothesis** - **Fail to reject the null hypothesis** #### e. Concluding the Hypothesis Test Your conclusion from the hypothesis test could be one of the following: - **There is sufficient evidence to warrant rejection of the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.** - **There is not sufficient evidence to warrant rejection of the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.** - **The sample data support the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.** - **There is not sufficient sample evidence to support the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.**
You manage two call centers and are working on trying to reduce the amount of time customers are placed on hold. You believe the mean hold times at the two call centers are not the same so you start by testing the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.

You wish to test the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2 at a significance level of \(\alpha = 0.002\).

You obtain the following two samples of data from each center. Each data point is the amount of time (in seconds), a customer is placed on hold.

| Call Center 1 | Call Center 2 |
|---------------|---------------|
| 79.1          | 103.8         |
| 84.8          | 73.0          |
| 86.8          | 87.0          |
| 84.2          | 64.1          |
| 62.1          | 65.2          |
| 81.3          | 94.7          |
| 79.1          | 80.6          |
| 48.7          | 118.6         |
| 60.6          | 94.7          |
| 83.0          | 77.7          |
| 47.8          | 73.0          |
| 112.4         | 94.2          |
| 77.1          | 51.9          |
|               | 111.1         |

**Questions:**

a. What is the test statistic for this sample?
- test statistic = ___ Round to 4 decimal places.

b. What is the p-value for this sample?
- p-value = ___ Round to 4 decimal places.

c. The p-value is...
- [ ] less than (or equal to) \(\alpha\)
- [ ] greater than \(\alpha\)
Transcribed Image Text:You manage two call centers and are working on trying to reduce the amount of time customers are placed on hold. You believe the mean hold times at the two call centers are not the same so you start by testing the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2. You wish to test the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2 at a significance level of \(\alpha = 0.002\). You obtain the following two samples of data from each center. Each data point is the amount of time (in seconds), a customer is placed on hold. | Call Center 1 | Call Center 2 | |---------------|---------------| | 79.1 | 103.8 | | 84.8 | 73.0 | | 86.8 | 87.0 | | 84.2 | 64.1 | | 62.1 | 65.2 | | 81.3 | 94.7 | | 79.1 | 80.6 | | 48.7 | 118.6 | | 60.6 | 94.7 | | 83.0 | 77.7 | | 47.8 | 73.0 | | 112.4 | 94.2 | | 77.1 | 51.9 | | | 111.1 | **Questions:** a. What is the test statistic for this sample? - test statistic = ___ Round to 4 decimal places. b. What is the p-value for this sample? - p-value = ___ Round to 4 decimal places. c. The p-value is... - [ ] less than (or equal to) \(\alpha\) - [ ] greater than \(\alpha\)
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