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. 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 it controls for any learning that may occur in using the simulator 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 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. Data Table - 1 3 4 Subject Normal, 4.49 Impaired, Y 5.86 2 4.34 5 4.31 4.58 4.65 6 7 8 9 4.83 4.59 5.00 4.79 5.49 5.23 5.61 5.63 5.67 5.45 5.29 5.90 Print Done

Answer 1

1)

a)v

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

b)

S. No Impaired Normal diff:(d)=x1-x2 12 1 5.86 449 1.37 1.88 2 5.67 1.33 1.77 3 5.45 4.34 4.58 4.65 0.87 0.76 4 5.29 0.64 0.41 5 5.9 4.31 1.59 2.53 6 5.49 4.83 0.66 0.44 7 5.23 4.59 0.64 0.41 00 5.61 5 0.61 0.37 9 0.71 Ed2=9.2633 5.63 4.79 total mean dbar degree of freedom -n-1 Std deviaiton S=v(Ed?-(Ed)*/n)/(n-1) = std error=Se=s./vn= 0.84 Ed=8.55 0.9500 8 0.377624 0.1259

for 95% CI; and 8 degree of freedom, value of t=			2.306
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		0.2903
lower confidence limit                     =		0.660
upper confidence limit                    =		1.240

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

2)

std error =√(S21/n1+S22/n2)=

0.4937

Point estimate of differnce =x1-x2     =		1.340
for 90 % CI & 39 df value of t=		1.685	from excel: t.inv(0.95,39)
margin of error E=t*std error                   =		0.832
lower bound=mean difference-E     =		0.5081
Upper bound=mean differnce +E      =		2.1719
from above 90% confidence interval for population mean =from 0.52 to 2.17

D. There is 90% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours.