Exploring Gender Differences in Driving Behaviors Among College Students
The Statistical Question
A psychologist was interested in exploring whether or not male and female college students have different driving behaviors. One of the ways to quantify this behavior was by focusing on the fastest speed ever driven by an individual. The statistical question she framed was: "Is the mean fastest speed driven by male college students different than the mean fastest speed driven by female college students?"
Survey Results
She conducted a survey of a random 29 male college students and a random 24 female college students. Here is a summary of the results:
- Males: Sample Size: 29, Mean: 105.5, Standard Deviation: 12.2
- Females: Sample Size: 24, Mean: 90.9, Standard Deviation: 20.1
(a) Are the variations of the fastest speeds for males and females the same? Provide all steps.
The variations of the fastest speeds for males and females are not the same. Comparing their standard deviations reveals that the standard deviation for males is 12.2, while the standard deviation for females is 20.1. Since the standard deviations are different, we can conclude that the variations of the fastest speeds for males and females are not the same.
(b) Based on (a), answer the psychologist's statistical question above. Provide all steps using the 3 methods. Final answer:
Based on the given data, we can use the t-test, z-test, or confidence interval to determine if the mean fastest speed driven by male college students is different than the mean fastest speed driven by female college students.
Explanation:
Comparing Variations: To determine if the variations are the same, we compare standard deviations. Since they are different, the variations are not the same.
Comparing Means: We can use the t-test, z-test, and confidence interval.
- T-Test: Compares means and determines statistical significance. Calculate t-value and p-value.
- Z-Test: Similar to t-test but for large sample sizes, which is not the case here.
- Confidence Interval: Calculate confidence intervals to determine if means overlap or not.
End result: The variations are different, and further testing could confirm if the mean fastest speeds are significantly different between genders.