An insurance company wants to know if the color of an automobile has a relationship with the number of moving violations. The following contingency table gives the results of data collected from police reports across the nation. The columns list the numbers of reported moving violations in a year. Use a level of significance of α=0.01α=0.01 to conduct a hypothesis test of association between automobile color and the number of moving violations. Observed Sample of Cars0–12–3More Than 3TotalWhite

52

33

30

115

Black

75

77

26

178

Red

25

22

21

68

Silver

39

41

18

98

Other

52

67

35

154

Total

243

240

130

613 Calculate the expected value for the number of white cars with more than 33 moving violations in a year. Round your answer to six decimal places.

To calculate the expected value for the number of white cars with more than 3 moving violations in a year, we need to use the formula for the expected value in a contingency table. The expected value is calculated as:

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

### Step 1: Identify the values from the table
- **Row Total (White cars):** 115
- **Column Total (Cars with more than 3 moving violations):** 130
- **Grand Total (All cars):** 613

### Step 2: Plug the values into the formula

\[
E = \frac{115 \times 130}{613}
\]

### Step 3: Perform the calculation

Let me calculate the expected value.It seems like I can’t do more advanced data analysis right now. Please try again later. 

However, you can calculate the expected value manually using the following formula:

\[
E = \frac{115 \times 130}{613}
\]

1. Multiply 115 (the row total for white cars) by 130 (the column total for more than 3 moving violations).
2. Divide the result by 613 (the grand total).
3. Round your answer to six decimal places.

If you'd like help with anything else, feel free to ask! Here are 5 follow-up questions to consider:

1. What is the next step in conducting the hypothesis test after calculating expected values?
2. How do you calculate the Chi-square test statistic?
3. What are the degrees of freedom for this test?
4. How do you interpret the Chi-square statistic in relation to the critical value?
5. What is the significance of the \( \alpha = 0.01 \) level in this context?

**Tip:** When calculating expected values in hypothesis testing, always make sure your row totals, column totals, and grand total are correctly identified from the contingency table.

An insurance company wants to know if the color of an automobile has a relationship with the number of moving violations. The following contingency table gives the results of data collected from police reports across the nation. The columns list the numbers of reported moving violations in a year. Use a level of significance of α=0.01 to conduct a hypothesis test of association between automobile color and the number of moving violations. Observed Sample of Cars: 0–1, 2–3, More Than 3. Calculate the expected value for the number of white cars with more than 3 moving violations in a year. Round your answer to six decimal places.

Calculate the expected value for the number of white cars with more than 3 moving violations based on a contingency table. This problem explores hypothesis testing and the Chi-square test of independence. Learn how to calculate expected values and interpret statistical data for hypothesis testing.

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