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To determine if there is a significant difference in the braking distances between Model A and Model B of high-end sedans, we'll perform a paired t-test. This test is suitable because the same drivers are used for both models, making the data paired. Here are the steps we will follow:

1. **Calculate the differences** in braking distances between Model A and Model B for each driver.
2. **Compute the mean** of these differences.
3. **Calculate the standard deviation** of these differences.
4. **Compute the t-statistic** using the formula: 
   \[
   t = \frac{\bar{d}}{s_d / \sqrt{n}}
   \]
   where \(\bar{d}\) is the mean difference, \(s_d\) is the standard deviation of the differences, and \(n\) is the number of pairs (drivers).

5. **Compare the t-statistic** to the critical value from the t-distribution (with \(n-1\) degrees of freedom) at a significance level of \(\alpha = 0.01\).

Let's begin by calculating the differences between the braking distances, and then proceed with the further steps.The computed t-statistic is approximately \(-2.336\) based on the differences in braking distances between Model A and Model B.

Would you like further details on how to interpret this result or proceed with checking the significance of this t-statistic using the t-distribution?

Here are some additional questions you might consider:
1. What is the critical t-value for a 0.01 significance level with 5 degrees of freedom?
2. How would the hypothesis be stated for this paired t-test?
3. What assumptions are necessary for conducting a paired t-test?
4. What would be the effect of increasing the sample size on the test results?
5. How could the data collection be improved to ensure more reliable results?

**Tip**: Always ensure the assumptions of normality and independence within pairs are reasonably met when performing a paired t-test.

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. Use alpha = 0.01. Can the auto dealer conclude that there is a significant difference in the braking distances of the two models?

This problem involves determining whether there's a significant difference in braking distances between two high-end sedan models. Using a paired t-test at a 0.01 significance level, we analyze the braking distance data from six drivers.

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