21.7: Find a​ 95% confidence interval for this difference and interpret it in context.

Question

In analyzing the city and highway fuel efficiencies of many cars and​ trucks, the mean difference in fuel efficiencies for the 632 vehicles was 7.36 mpg with a standard deviation of 2.59 mpg. Find a​ 95% confidence interval for this difference and interpret it in context.

The​ 95% confidence interval for the difference in fuel efficiencies is ( , )mpg.

​(Round to two decimal places as​ needed.)

Answer 1

95% CI is mean +- z- critical value * standard deviation/sqrt(sample size)

mean is 7.36

z-critical value for 95% CI = 1.96

standard deviation is 2.59

sample size = 632

substituting into equation you get:

7.36 +- 1.96 * 2.59/sqrt(632)

7.16, 7.56