Question

In analyzing the city and highway fuel efficiencies of many cars and trucks, the mean difference in fuel efficiencies for the 642 vehicles was 7.45 mpg with a standard deviation of 2.46 mpg. Find a 95% confidence interval for this difference and interpret it in context.

Answer 1

To find a 95% confidence interval for the difference in fuel efficiencies, use the formula: CI = (mean difference) ± (critical value) × (standard deviation difference).

Substitute the given values and calculate the confidence interval. Interpret the confidence interval as being 95% confident that the true mean difference falls between the lower and upper bounds.

Step-by-step explanation:

To find a 95% confidence interval for the difference in fuel efficiencies, we can use the formula:
CI = (mean difference) ± (critical value) × (standard deviation difference)
First, we need to determine the critical value for a 95% confidence interval. Since we have a large sample size (642 vehicles) and assume the data is normally distributed, we can use a z-score. The z-score for a 95% confidence interval is approximately 1.96.
Next, we substitute the given values into the formula:
CI = (7.45) ± (1.96) × (2.46)
Calculating the values:
CI = (7.45) ± (4.81)
Finally, we can interpret the confidence interval. The 95% confidence interval for the mean difference in fuel efficiencies is (2.64, 12.26) mpg. This means that we are 95% confident that the true mean difference in fuel efficiencies for all vehicles falls between 2.64 and 12.26 mpg.