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.

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

Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the experiment? (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." State the appropriate conclusion.

Subject Normal,Xi Impaired, Yi

1 4.49 5.86

2 4.24 5.67

3 4.58 5.51

4 4.56 5.29

5 4.31 5.90

6 4.80 5.49

7 4.59 5.23

8 5.00 5.61

9 4.79 5.63

Answer 1

Here we have to perform 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.so that we will get the positive differences d = impaired - normal

b)

To find 95% confidence interval first we need to find sample mean and sample sd for difference d = impaired minus normal.

We can find it using excel as follows ,

Therefore sample mean ( ) = 0.98

Sample sd ( ) = 0.3788

To find 95% Confidence interval we can use TI-84 calculator,

Press STAT ----> Scroll to TESTS ---- > Scroll down to 8: T Interval and hit enter.

Then select Stats and hit enter , plug the values accordingly,

Therefore we are 95% confident that mean difference in braking time with impaired vision and normal vision is between ( 0.6888 , 1.2712)

Conclusion : As both values in the interval are greater than 0 , mean difference impaired minus normal is not equal to 0

There is significant evidence that  there is a difference in braking time with impaired vision and normal vision at 95% confidence level .