Chapter 3: Q 81. (page 197)

Marijuana and traffic accidents (1.1) Researchers in New Zealand interviewed $907$ drivers at age $21$
They had data on traffic accidents and they asked the drivers about marijuana use. Here are data on the numbers of accidents caused by these drivers at age $19$ , broken down by marijuana use at the same age
(a) Make a graph that displays the accident rate for each class. Is there evidence of an association
between marijuana use and traffic accidents?
(b) Explain why we can’t conclude that marijuana use causes accidents.

Short Answer

Expert verified

Part (a) The graph that determines the accident rate for each class is as below:

There is evidence of a link between marijuana usage and road accidents because the height of the bars rises as the annual marijuana consumption rises.

Part (b) We can't prove causation because we don't know if the subjects were driving under the influence of marijuana at the time of the accident, and people may be lying about their marijuana use.

Step by step solution

Part (a) Step 1: Given information

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

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

Concept

To begin, use the below equation to calculate the accident rate for each class, and then construct a histogram to depict it. Finally, utilize the histogram to determine whether there is evidence of a link between marijuana use and road accidents.

Accidents caused in each class $= \frac{A c c i d e n t s C a u s e d}{D r i v e r s}$

Part (a) Step 3: Calculation

Determine the ratio of accidents caused in each group: $N e v e r : \frac{A c c i d e n t s C a u s e d}{D r i v e r s} = \frac{59}{452} \approx 0.1305 1 - 10 t i m e s : \frac{A c c i d e n t s C a u s e d}{D r i v e r s} = \frac{36}{229} \approx 0.1572 11 - 50 t i m e s : \frac{A c c i d e n t s C a u s e d}{D r i v e r s} = \frac{15}{70} \approx 0.2143 51 + t i m e s : \frac{A c c i d e n t s C a u s e d}{D r i v e r s} = \frac{50}{156} \approx 0.3205$

Create a histogram in which the width of all bars is the same and the height is the same as the ratio.

There is evidence of a link between marijuana usage and road accidents because the height of the bars grows as the annual marijuana consumption increases.

Part (b) Step 1: Explanation

There could be hidden variables influencing the study's outcomes, such as overall drug use and interest in safe driving. A hidden variable is one that has a significant impact on the relationship between variables in a study but is not one of the explanatory factors investigated. As a result, we can't prove causality because we don't know if the subjects were driving under the influence of marijuana when they caused the accident, and people may lie about their marijuana use.