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This problem involves performing a hypothesis test to determine if there is a significant difference in the braking distances of two models of high-end sedans. Given that we are provided with data for braking distances across six drivers for both Model A and Model B, we will conduct a **paired t-test** since the same drivers are testing both models, making it a dependent sample.

### Hypotheses for the test:
- **Null Hypothesis (\(H_0\))**: There is no significant difference in the braking distances between Model A and Model B, i.e., the mean difference \( \mu_d = 0 \).
- **Alternative Hypothesis (\(H_1\))**: There is a significant difference in the braking distances between the two models, i.e., \( \mu_d \neq 0 \).

We are given:
- Significance level \( \alpha = 0.01 \).
- Braking distances for both Model A and Model B across six drivers.

The formula for the **test statistic (t)** in a paired t-test is:

\[
t = \frac{\bar{d}}{s_d / \sqrt{n}}
\]

Where:
- \( \bar{d} \) is the mean of the differences between the paired samples (Model A - Model B),
- \( s_d \) is the standard deviation of the differences,
- \( n \) is the number of paired samples (in this case, 6).

Let me calculate the test statistic now.It seems like I can’t do more advanced data analysis right now. Please try again later. If you prefer, I can guide you through the steps manually to calculate the test statistic. Let me know how you'd like to proceed!

Would you like more details, or do you have any questions so far?

Here are five questions to expand on what we've covered:
1. What are the assumptions of a paired t-test?
2. How does the significance level \( \alpha \) affect the decision in hypothesis testing?
3. What happens if the calculated p-value is greater than the significance level?
4. Can the paired t-test be used if the sample size is large?
5. What is the importance of standard deviation in hypothesis testing?

**Tip**: In paired t-tests, always check if the data are normally distributed, especially for small sample sizes.

An auto dealer would like to determine if there is a difference in the braking distance (the number of feet required to go from 60 mph to 0 mph) of two different models of a high-end sedan. Six drivers are randomly selected and asked to drive both models and brake once they have reached exactly 60 mph. The distance required to come to a complete halt is measured in feet. The results of the test are as follows. Can the auto dealer conclude that there is a significant difference in the braking distances of the two models? Use α = 0.01.

This problem explores whether there is a significant difference in braking distances between two models of high-end sedans. We conduct a paired t-test based on data from six drivers for both models at a significance level of α = 0.01.

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