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 E! Click the icon to view the data table (a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the experiment? O 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. 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)

Answer 1

a)

Dependent sample t test

Therefore wore goggles first was randomly selected because the reaction time in an emergency taken with goggles would be greater than reaction time in an emergency taken with unimpaired vision

d = impaired - normal

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

b)

n = 9

S.No	Normal, Xi	Impaired, Yi	d = Yi - Xi
1	4.49	5.77	1.28
2	4.24	5.67	1.43
3	4.58	5.51	0.93
4	4.65	5.32	0.67
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
Total	41.44	50.13	8.69
mean	4.60444444	5.57	0.965556
St.Dev			0.372529
Confidence Interval	0.96555556
t(n-1, 0.966)	2.10880149
Upper Limit	1.22741872
Lower Limit	0.70369239

mean difference impaired - normal is not equal to 0

Point of estimate = ( mean of Yi - mean of Xi )

$\pm(t_{n-1,a/2}*\frac{s}{\sqrt{n}})$

The interval are greater than 0 ,

Therefore we are 95% confident that mean difference in braking time with impaired vision and normal vision is between ( 0.7037 , 1.2274 )

The Lower bound is 0.7037

The Upper bound is 1.2274