Question

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 category of marijuana use. Is there evidence of an association between marijuana use and traffic accidents? Justify your answer.

b. Explain why we can’t conclude that marijuana use causes accidents based on this study.

Short answer

Part (a) Yes, there is evidence.

Part (b) 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.

Step-by-step solution

Part (a) Step 1: Given information

Part (a) Step 2: Calculation

Now, the ratio of the accidents in each group will be as:

Never:

$$\begin{gathered} \frac{59}{452}=0.1305 \\ 1-10times:\frac{36}{229}=0.1572 \\ 11-50times:\frac{15}{70}=0.2143 \\ 51+times:\frac{50}{156}=0.3205 \end{gathered}$$

Part (a) Step 3: Explanation

Thus the histogram of the data will be as:

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

We can't prove causality since we don't know if the individuals were driving under the influence of marijuana when they caused the accident, and they may be lying about their marijuana use. Furthermore, variables such as overall drug usage and interest in safe driving could influence the study's findings. 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.