Question

In an experiment at Ohio State University in 1986, 16 students consumed varying amounts of beer. The amount each student consumed was randomly determined. Thirty minutes after finishing the last beer, the students took a Breathalyzer test to measure their blood alcohol level (BAL). BAL is measured by percent of alcohol in the blood. A police officer also gave each student four field sobriety tests. The tests included balancing on one foot, touching the tip of one’s nose with the forefinger, tipping one’s head back with eyes closed, and walking heel to toe. The officer was unaware of each student’s BAL and graded each test on a 1-10 scale. The scores for the four tests were averaged together.

The table below gives the BAL and sobriety test average for each of the 16 students.

Blood Alcohol Level (%)	0.1	0.03	0.19	0.12	0.04	0.095	0.07	0.06
Field Sobriety Test Avg	6	9.25	4.75	7.5	9.75	6.5	7	8.75

1. Interpret the slope in the context of the problem, using the correct units. Be careful how you interpret this.

2. The legal limit for driving while intoxicated is 0.08%. What does the regression line predict as the field sobriety test average for someone with a BAL at the legal limit?

3. How many students scored lower than your answer for (2) despite not being legally intoxicated?

4. What is the predicted field sobriety test average for the student with a blood alcohol level of .12?

5. Find the residual for the individual in question #4.

Answer 1

1. Interpret the slope in the context of the problem, using the correct units. Be careful how you interpret this.

As the Blood Alcohol Level (BAL) increases, the field sobriety test average decreases by 21.867.

1. The legal limit for driving while intoxicated is 0.08%. What does the regression line predict as the field sobriety test average for someone with a BAL at the legal limit?

y = -21.867*0.08 + 9.410 = 7.66

1. How many students scored lower than your answer for (2) despite not being legally intoxicated?

5 students

1. What is the predicted field sobriety test average for the student with a blood alcohol level of .12?

y = -21.867*0.12 + 9.410 = 6.79

1. Find the residual for the individual in question #4.

Residual = 7.5 - 6.79 = 0.71