Question

Subject	1	2	3	4	5	6	7	8	9
​Normal, Upper X Subscript iXi	4.494.49	4.344.34	4.584.58	4.564.56	4.314.31	4.834.83	4.594.59	5.005.00	4.794.79
​Impaired, Upper Y Subscript iYi	5.775.77	5.675.67	5.515.51	5.295.29	5.905.90	5.495.49	5.235.23	5.615.61	5.635.63

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.

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​(a) Whether the student had the 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

nothing.

The upper bound is

nothing.

​(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

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

b)

normal	impaired	d
4.49	5.77	-1.28
4.34	5.67	-1.33
4.58	5.51	-0.93
4.56	5.29	-0.73
4.31	5.9	-1.59
4.83	5.49	-0.66
4.59	5.23	-0.64
5	5.61	-0.61
4.79	5.63	-0.84
	mean	-0.95667
	sd	0.356931
	n	9
	t	2.306004

The 95% confidence interval is −1.231<μD​<−0.682

lower bound = -1.231

upper bound = -0.682
c)

since 0 is not present in confidence interval

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