Question

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. Complete parts​ (a) and​ (b).

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

Subject   Normal, Xi   Impaired, Yi
1   4.47   5.86
2   4.24   5.67
3   4.58   5.51
4   4.65   5.32
5   4.31   5.83
6   4.83   5.49
7   4.59   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?

A.

This is a good idea in designing the experiment because reaction times are different.

B.

This is a good idea in designing the experiment because the sample size is not large enough.

C.

This is a good idea in designing the experiment because it controls for any​ "learning" that may occur in using the simulator.

​

(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."

The lower bound is __?__.

The upper bound is __?__.

​(Round to the nearest thousandth as​ needed.)

State the appropriate conclusion. Choose the correct answer below.

There is insufficient evidence to conclude there is a difference in braking time with impaired vision and normal vision.

There is sufficient evidence to conclude there is a difference in braking time with impaired vision and normal vision.

Answer 1

The statistical software output for this problem is:

Hence,

a) This is a good idea in designing the experiment because it controls for any​ "learning" that may occur in using the simulator.

​Option C is correct.

b) Lower bound = 0.680

Upper bound = 1.255

Conclusion: There is sufficient evidence to conclude there is a difference in braking time with impaired vision and normal vision. Option B is correct.