To illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school.

To illustrate the effects of driving under the influence​ (DUI) of​ alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine​ teenagers, the time​ (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded.

​Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

Data:

Subject                Normal, Xi                 Impaired, Yi

1                           4.49                              5.77

2                           4.34                              5.85

3                           4.58                              5.51

4                           4.65                              5.29

5                           4.31                              5.90

6                           4.80                              5.49

7                           4.55                              5.23

8                           5.00                              5.63

9                           4.79                              5.63

(A) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the​ experiment?

(B) Use a​ 95% confidence interval to test if there is a difference in braking time with impaired vision and normal vision where the differences are computed as​ "impaired minus​ normal."

(C) State the appropriate conclusion.