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A large car insurance company is conducting a study on behavior behind the wheel to explain the fact that male drivers (who tend to be thought of as more aggressive drivers) have more accidents, on average, per year, than female drivers. The average number of accidents per year for male drivers is 2.3 with a standard deviation of 0.8 and for female drivers the mean is 1.7 with a standard deviation of 0.6. Independent random samples of 25 male and 20 female drivers are to be selected to take part in the behavior study.
-If the sample mean number of accidents is to be calculated for both the male and female drivers and we calculate the difference as male - female, what is the standard deviation of the sampling distribution of the difference in sample means?
A) 0.0436
B) 0.2088
C) 0.2942
D) 0.7

Question

Use the following information for questions:
 A large car insurance company is conducting a study on behavior behind the wheel to explain the fact that male drivers (who tend to be thought of as more aggressive drivers) have more accidents, on average, per year, than female drivers. The average number of accidents per year for male drivers is 2.3 with a standard deviation of 0.8 and for female drivers the mean is 1.7 with a standard deviation of 0.6. Independent random samples of 25 male and 20 female drivers are to be selected to take part in the behavior study.
-If the sample mean number of accidents is to be calculated for both the male and female drivers and we calculate the difference as male - female, what is the standard deviation of the sampling distribution of the difference in sample means?
A) 0.0436
B) 0.2088
C) 0.2942
D) 0.7

Quizplus · Accepted Answer

The standard deviation of the sampling distribution of the difference between two independent means is calculated using the formula: $\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$, where $\sigma_1$ and $\sigma_2$ are the standard deviations of the two populations, and $n_1$ and $n_2$ are the sample sizes. Plugging in the given values: $\sqrt{\frac{0.8^2}{25} + \frac{0.6^2}{20}} = \sqrt{\frac{0.64}{25} + \frac{0.36}{20}} = \sqrt{0.0256 + 0.018} = \sqrt{0.0436} = 0.2088$.

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