Steve thinks he can drive legally 30 minutes after he drinks 5 beers. The legal limit is BAC = 0.08. Give a 90% prediction interval for Steve’s BAC. Can he be confident he won’t be arrested if he drives and is stopped?

How well does the number of beers a student drinks predict his or her blood alcohol content (BAC)? Sixteen student volunteers at Ohio State University drank a randomly assigned number of 12-ounce cans of beer. Thirty minutes later, a police officer measured their BAC. Here are the data. The students were equally divided between men and women and differed in weight and usual drinking habits. Because of this variation, many students don’t believe that number of drinks predicts BAC well.

answer:

prediction interval : (0.040 , 0.114)

Step-by-step explanation:

Given data:

Confidence level = 90%

Legal limit ( BAC ) = 0.08

solution

sample size = 16

Degree of freedom ( df ) = 14

critical t value = 1.761

X = 4.81

Σ(x-x)² (Sx) = 72.44

also standard error of estimates = 0.0204

Y= -0.01270 + 0.01796 * 5 = 0.077

given that ; the predicted value of Y at x = 5

Considering individual response Y

standard error = 0.0211

margin of error = 1.761 * 0.021 = 0.0371

Hence the limits of the prediction interval is :

Lower limit = 0.077 - 0.037 = 0.040.

Upper limit = 0.077 + 0.037 = 0.114

Finally

90% prediction interval = (0.040 , 0.114)