To determine if running red lights and speeding are not independent events, we need to calculate the expected frequencies for each cell based on the assumption of independence.

Steps:

1. Calculate the row totals, column totals, and grand total.
2. Use the formula for expected frequency: $\text{Expected Frequency} = \frac{(\text{Row Total} \times \text{Column Total})}{\text{Grand Total}}$

Given Data:

	Speeding	Not Speeding	Row Totals
Ran red-light	62	84	146
Did not run red-light	31	23	54
Column Totals	93	107	200

Calculations:

1. Grand Total = $200$
2. Expected Frequencies:
   • For $(\text{Ran red-light, Speeding})$: $\text{Expected} = \frac{(146 \times 93)}{200} = 67.89$
   • For $(\text{Ran red-light, Not Speeding})$: $\text{Expected} = \frac{(146 \times 107)}{200} = 78.11$
   • For $(\text{Did not run red-light, Speeding})$: $\text{Expected} = \frac{(54 \times 93)}{200} = 25.11$
   • For $(\text{Did not run red-light, Not Speeding})$: $\text{Expected} = \frac{(54 \times 107)}{200} = 28.89$

Final Table:

	Speeding	Not Speeding	Row Totals
Ran red-light	67.89	78.11	146
Did not run red-light	25.11	28.89	54
Column Totals	93	107	200

Would you like me to proceed with further analysis to test for independence, such as conducting a chi-square test?

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5 Related Questions:

1. What is the formula for calculating expected frequencies in a contingency table?
2. How do you interpret the results of a chi-square test for independence?
3. Why is it important to test for independence between two events?
4. Can you explain the conditions under which the chi-square test is valid?
5. What do row and column totals represent in a contingency table?

Tip:

When solving problems involving contingency tables, double-check totals to ensure calculations are consistent with the given data.