How well does the number of beers a student drinks predict his or her blood alcohol

content? In a study at Ohio State University, 16 student volunteers drank

a randomly assigned number of cans of beer. Thirty minutes later, a police officer

measured their blood alcohol content (BAC) in grams of alcohol per deciliter

of blood. Here are the data:

Student 1 2 3 4 5 6 7 8

Beers 5 2 9 8 3 7 3 5

BAC 0.10 0.03 0.19 0.12 0.04 0.095 0.07 0.06

Student 9 10 11 12 13 14 15 16

Beers 3 5 4 6 5 7 1 4

BAC 0.02 0.05 0.07 0.10 0.085 0.09 0.01 0.05

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 blood alcohol well.

(a) Make a scatterplot of the data. Find the equation of the least-squares regression line for predicting blood alcohol from number of beers and add this line to your plot. What is R^2 for these data? Briefly summarize what your data analysis shows.

(b) Is there a significant evidence that drinking more beers increases blood alcohol on the average in the population of all students? State hypotheses, give a test statistic and P-value, and state your conclusion.

content? In a study at Ohio State University, 16 student volunteers drank

a randomly assigned number of cans of beer. Thirty minutes later, a police officer

measured their blood alcohol content (BAC) in grams of alcohol per deciliter

of blood. Here are the data:

Student 1 2 3 4 5 6 7 8

Beers 5 2 9 8 3 7 3 5

BAC 0.10 0.03 0.19 0.12 0.04 0.095 0.07 0.06

Student 9 10 11 12 13 14 15 16

Beers 3 5 4 6 5 7 1 4

BAC 0.02 0.05 0.07 0.10 0.085 0.09 0.01 0.05

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 blood alcohol well.

(a) Make a scatterplot of the data. Find the equation of the least-squares regression line for predicting blood alcohol from number of beers and add this line to your plot. What is R^2 for these data? Briefly summarize what your data analysis shows.

(b) Is there a significant evidence that drinking more beers increases blood alcohol on the average in the population of all students? State hypotheses, give a test statistic and P-value, and state your conclusion.

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