DUI Simulator: 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 special pair of goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. The data including the difference score Impaired - Normal appears in the table below. The mean and standard deviation of the difference scores are xd = 0.963 and sd = 0.358

Normal 4.47 4.24 4.58 4.65 4.31 4.80 4.55 5.00 4.79

Impaired 5.77 5.67 5.51 5.32 5.83 5.49 5.23 5.61 5.63

Impaired - Normal 1.30 1.43 0.93 0.67 1.52 0.69 0.68 0.61 0.84

(a) Compute the 95% confidence interval for d.

(b) Interpret the interval in context. Be sure to provide an indication of the direction of the difference.

Please show all of your work and formulas.