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.
subject 1 2 3 4 5 6 7 8 9
normal, xi 4.47 4.24 4.58 4.65 4.31 4.80 4.55 5.00 4.79
impaired, yi 5.77 5.67 5.51 5.32 5.83 5.49 5.23 5.61 5.6
(a) 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. "note: a normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

a) If we design the experiment on this way we can check if we have an improvement with the method used.

We assume that we have the same individual and we take a value before with the normal impaired condition and the final condition is the normal case.  

b)  

The 95% confidence interval would be given by (-1.24;-0.69)

Step-by-step explanation:

Part a

If we design the experiment on this way we can check if we have an improvement with the method used.

We assume that we have the same individual and we take a value before with the normal impaired condition and the final condition is the normal case.

Part b

For this case first we need to find the differences like this :

Normal, Xi 4.47 4.24 4.58 4.65 4.31 4.80 4.55 5.00 4.79

Impaired, Yi 5.77 5.67 5.51 5.32 5.83 5.49 5.23 5.61 5.6

Let

The second step is calculate the mean difference  

The third step would be calculate the standard deviation for the differences, and we got:

The confidence interval for the mean is given by the following formula:  

(1)  

In order to calculate the critical value we need to find first the degrees of freedom, given by:  

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that  

Now we have everything in order to replace into formula (1):  

So on this case the 95% confidence interval would be given by (-1.24;-0.69)

the correct answer is c