Question

To illustrate the effects of driving under the influence 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 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 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.Data table:Subj. 1 2 3 4 5 6 7 8 9Normal 4.49 4.24 4.58 4.56 4.31 4.80 4.59 5.00 4.79XiImpaired 5.86 5.85 5.45 5.32 5.90 5.49 5.23 5.63 5.63XiA. (pick one below)a. This is a good idea in designing the experiment because the sample size is not large enough.b. This is a good idea in designing the experiment because reaction times are different.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 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 95% confidence interval is (_, _). (Round to the nearest thousandth as needed.)State the appropriate conclusion. Choose the correct answer below.a. There is sufficient evidence to conclude there is a difference in braking time with impaired vision and normal vision.b. There is insufficient evidence to conclude there is a difference in braking time with impaired vision and normal vision.

Answer 1

Answer:

Check the explanation

Step-by-step explanation:

Here we have to first of all carry out dependent sample t test. consequently wore goggles first was selected at random for the reason that the reaction time in an emergency taken with goggles would be greater than the amount of reaction time in an emergency taken with not so weakened 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 that is in the first attached image below,

Therefore sample mean $( \bar{X}_{d} )$ = 0.98

Sample sd $( \bar{S}_{d} )$ = 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.

Kindly check the attached image below.

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 .