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   5.45
4   4.56   5.32
5   4.31   5.90
6   4.83   5.49
7   4.55   5.23
8   5.00   5.61
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 the sample size is not large enough.

B.

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

C.

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

​(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

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	NormalXi	ImpairedYi	difference( impaired-normal)
1	4.47	5.86	1.39
2	4.24	5.67	1.43
3	4.58	5.45	0.87
4	4.56	5.32	0.76
5	4.31	5.9	1.59
6	4.83	5.49	0.66
7	4.55	5.23	0.68
8	5	5.61	0.61
9	4.79	5.63	0.84

​(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 the sample size is not large enough.

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

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

​(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 0.689

The upper bound is 1.273

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

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	0.3795
Sample Mean	0.9811
Sample Size	9
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.1265
Degrees of Freedom	8
t Value	2.3060
Interval Half Width	0.2917
Confidence Interval
Interval Lower Limit	0.689
Interval Upper Limit	1.273

since 95% CI does not contain 0 value, there is significant difference.

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.

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