"Driver Fatalities The following data represent the number of drivers involved in a fatal crash in 2016 in various light and weather conditions.

c. Is the dark (without light) more dangerous in normal weather or in rain? Explain."

Verified step by step guidance

1. Identify the relevant data from the table for the 'Dark' light condition under both 'Normal' weather and 'Rain' weather. From the table, these values are 8151 for Normal weather and 681 for Rain weather.
2. Understand that the question asks which condition is more dangerous, so we need to compare the number of driver fatalities in the 'Dark' condition for Normal weather versus Rain weather.
3. Consider the total number of fatalities in each weather condition to provide context. For example, sum all fatalities under Normal weather and under Rain weather to see the overall scale of fatalities in each condition.
4. Calculate the proportion of fatalities that occur in the 'Dark' condition relative to the total fatalities for each weather type. This can be done using the formula: \(\text{Proportion} = \frac{\text{Fatalities in Dark}}{\text{Total Fatalities in that Weather}}\).
5. Compare these proportions to determine if 'Dark' conditions are more dangerous in Normal weather or in Rain. A higher proportion indicates a greater relative danger in that condition.

Key Concepts

Contingency Tables

A contingency table displays the frequency distribution of variables and helps analyze the relationship between categorical variables. In this question, the table shows driver fatalities categorized by weather and light conditions, allowing comparison across different scenarios.

Comparative Risk Analysis

Comparative risk analysis involves comparing the likelihood or frequency of an event under different conditions. Here, it means comparing the number of fatal crashes in 'Dark' conditions during 'Normal' weather versus 'Rain' to determine which is more dangerous.

Relative Frequency and Proportions

Relative frequency expresses the count of occurrences as a proportion of the total, providing a normalized basis for comparison. To assess danger accurately, one should consider fatal crashes relative to total crashes or exposure in each weather condition, not just raw counts.