# Proportion Hypothesis Test: Does Traffic School Reduce Moving Violations?

## Question:

Is the proportion of drivers with moving violations higher for those attending traffic school compared to those doing volunteer work?

## Answer:

The question pertains to mathematical statistics specifically a proportion hypothesis test. This involves carrying out a Z test by comparing the proportions of drivers with moving violations between traffic school attendees and volunteer workers. After calculating the Z score, we compare it with the critical Z score to determine if there is a significant difference in the occurrence of moving violations between the two groups.

## Explanation:

The subject of your question pertains to statistical testing, specifically a **proportion hypothesis test**. Here, we need to analyze whether attending traffic school has an effect on the rates of moving violations among high-risk drivers, by comparing the proportion of violations among those who attended traffic school and those who performed volunteer work.

First, we establish the null and alternate hypotheses. The null hypothesis: the proportion of drivers with moving violations is the same for both groups. And the alternate hypothesis: the proportion of drivers with moving violations for those attending traffic school is higher. We are using a one-tailed test because we are looking for a higher proportion among traffic school attendees (not a difference in either direction).

To calculate the **Z score**, you can use the formula:

Z = (p1 - p2) / sqrt [ ((p * q) / n1) + ((p * q) / n2) ]

In this formula, p1 and p2 are the proportions of each group (traffic school attendees and volunteers respectively), p is the combined proportion of both groups having a moving violation, n1 and n2 are the sample sizes, and q is 1-p (the proportion of each group not having a moving violation).

In conclusion, after calculating the Z score, if the absolute value is higher than the critical Z score from the standard Z table (which, at 0.05 significance level, is 1.645 for a one-tailed test), we can reject the null hypothesis and conclude that the proportion of drivers with moving violations is significantly different between traffic school attendees and those who performed volunteer work.