Chapter 3.2, Problem 81E

a.

To determine

To display a graph that determines the accident rate for each class. To determine whether there is the evidence of an association between marijuana use and traffic accidents.

Answer to Problem 81E

The graph that determines the accident rate for each class is as below:

Since the height of the bars increase as the marijuana use per year increases, there is an evidence of an association between marijuana use and traffic accidents.

Explanation of Solution

Given:

Here are the data on the number of accidents caused by the drivers using marijuana per year.

	Marijuana Use per Year
Never	1-10 times	11-50 times	51+ times
Drivers	452	229	70	156
Accidents Caused	59	36	15	50

Concept Used:

Firstly, need to determine the accident rate for each class by using the below equation, and then draw the histogram to represent it. Lastly, determine the evidence of an association between marijuana use and traffic accidents from the histogram obtained.

$\text{Accidents caused in each class}=\frac{\text{Accidents Caused}}{\text{Drivers}}$

Calculation:

Determine the ratio of accidents caused in each group:

$\begin{array}{l}\text{Never}:\frac{\text{Accidents Caused}}{\text{Drivers}}=\frac{59}{452}\approx 0.1305\\ \text{1-10 times}:\frac{\text{Accidents Caused}}{\text{Drivers}}=\frac{36}{229}\approx 0.1572\\ \text{11-50 times}:\frac{\text{Accidents Caused}}{\text{Drivers}}=\frac{15}{70}\approx 0.2143\\ \text{51+ times}:\frac{\text{Accidents Caused}}{\text{Drivers}}=\frac{50}{156}\approx 0.3205\end{array}$

Create a histogram, where in the width of all bars should be equal and the height should be equal to the ratio.

Since the height of the bars increase as the marijuana use per year increases, there is an evidence of an association between marijuana use and traffic accidents.

b.

To determine

To explain why it cannot be concluded that marijuana use causes accidents.

Answer to Problem 81E

We can't prove causation, because we don't know if the subjects drive under influence of marijuana when they cause an accident and people also might be untruthful about their marijuana use.

Explanation of Solution

There might be lurking variables such as overall drug use and interest in safe driving that affect the results of the study. A lurking variable is a variable that has an important effect on the relationship among the variables in a study but is not one of the explanatory variables studied.

Hence, we can't prove causation, because we don't know if the subjects drive under influence of marijuana when they cause an accident and people also might be untruthful about their marijuana use.