To conduct a hypothesis test of association between automobile color and the number of moving violations, we can use the Chi-Square Test of Independence. We are provided with a contingency table, and we need to compute the value of the test statistic.

Here is a step-by-step approach:

Step 1: Set up the observed values (O)

We already have the observed values from the contingency table.

Step 2: Compute the expected values (E)

The expected value for each cell is calculated using the formula:

$E = \frac{(\text{Row Total}) \times (\text{Column Total})}{\text{Grand Total}}$

We'll calculate the expected values for each cell:

$E_{ij} = \frac{(\text{Row Total for } i) \times (\text{Column Total for } j)}{613}$

For example, the expected value for the first cell (White, 0–1 violations) is:

$E_{White, 0-1} = \frac{115 \times 243}{613} = 45.585$

We'll compute all the expected values.

Step 3: Compute the Chi-Square test statistic

The Chi-Square test statistic is given by:

$\chi^2 = \sum \frac{(O - E)^2}{E}$

Where:

• $O$ is the observed value
• $E$ is the expected value

Let me calculate this now.The value of the test statistic for the Chi-Square test is $\chi^2 = 16.862$, rounded to three decimal places.

Would you like to see the next steps or have any questions on the process so far?

Here are five related questions that might interest you:

1. How do we determine the critical value for the Chi-Square test?
2. What are the degrees of freedom for this test?
3. How do we interpret the results of the Chi-Square test?
4. What assumptions are made when using the Chi-Square test of independence?
5. How would the test result change if we used a different significance level?

Tip: Ensure your expected values are sufficiently large (at least 5) to meet the assumptions of the Chi-Square test for reliable results.