To calculate the expected value for the number of white cars with 0-1 moving violations in a year, we can use the formula for expected frequency in a contingency table:

$E_{ij} = \frac{(Row \, Total) \times (Column \, Total)}{Grand \, Total}$

Where:

• $E_{ij}$ is the expected frequency for the cell corresponding to row $i$ and column $j$.
• $Row \, Total$ is the total number of cars in the particular row (for white cars in this case).
• $Column \, Total$ is the total number of cars in the particular column (for 0-1 moving violations in this case).
• $Grand \, Total$ is the total number of observations.

From the contingency table:

• Row Total for white cars: $64 + 65 + 26 + 155 = 310$
• Column Total for 0-1 moving violations: $64 + 56 + 77 + 61 + 44 = 302$
• Grand Total: $593$

Now, using the formula to find the expected value for the number of white cars with 0-1 moving violations:

$E_{\text{white, 0-1}} = \frac{(310) \times (302)}{593}$

Let's calculate this:

$E_{\text{white, 0-1}} = \frac{93620}{593} \approx 157.974115$

Thus, the expected value for the number of white cars with 0-1 moving violations is approximately 157.974115.

Would you like to proceed with the next step or need further clarification?

Related Questions:

1. How do we calculate the expected values for all the other cells in the table?
2. What is the next step in the hypothesis testing procedure after calculating the expected values?
3. What is the formula for the chi-square statistic in this case?
4. How do we interpret the results of a chi-square test?
5. Why is a significance level of 0.01 used in this test?

Tip:

When performing chi-square tests, always ensure that your expected values are sufficiently large (typically at least 5). If many cells have expected values less than 5, the test may not be reliable.