College Survey In a national survey conducted by the Centers for Disease Control to determine health-risk behaviors among college students, college students were asked, “How often do you wear a seat belt when driving a car?” The frequencies were as follows:

g. Compute the relative frequencies of “Never,” “Rarely,” “Sometimes,” “Most of the time,” and “Always,” excluding those that do not drive. Compare with those in Problem 13. What might you conclude?

Verified step by step guidance

1. Step 1: Identify the categories to include in the relative frequency calculation. Since the problem asks to exclude those who 'do not drive a car,' remove the frequency for 'I do not drive a car' from the total count.
2. Step 2: Calculate the total number of respondents who drive by summing the frequencies of the categories 'Never,' 'Rarely,' 'Sometimes,' 'Most of the time,' and 'Always.' Use the formula: \(\text{Total drivers} = 118 + 249 + 345 + 716 + 3093\).
3. Step 3: Compute the relative frequency for each category by dividing the frequency of that category by the total number of drivers. For example, for 'Never,' the relative frequency is \(\frac{118}{\text{Total drivers}}\).
4. Step 4: Repeat the calculation for each category ('Rarely,' 'Sometimes,' 'Most of the time,' and 'Always') using the same method: \(\text{Relative frequency} = \frac{\text{Frequency of category}}{\text{Total drivers}}\).
5. Step 5: Compare the relative frequencies you calculated with those from Problem 13 (if available) to analyze any differences or trends in seat belt usage among college students. Consider what the relative frequencies suggest about the behavior of drivers in this survey.

Key Concepts

Relative Frequency

Relative frequency is the proportion of times a particular event occurs compared to the total number of observations, often expressed as a fraction or percentage. It is calculated by dividing the frequency of a specific category by the total frequency of all relevant categories, providing insight into the distribution of responses.

Excluding Categories in Analysis

When analyzing survey data, certain categories may be excluded to focus on a relevant subset. In this case, excluding 'I do not drive a car' ensures the relative frequencies reflect only those who drive, making the analysis more meaningful and accurate for understanding seat belt usage among drivers.

Comparative Analysis

Comparative analysis involves comparing results from different data sets or problems to identify trends, differences, or similarities. Here, comparing relative frequencies with those from Problem 13 helps draw conclusions about changes or consistencies in seat belt usage behavior among college students over time or across samples.