C21.7: 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

Since sample size is large can use z-critical value

CI = difference in means +- z-critical * standard deviation/square root (sample size)

difference in means is 7.36, standard deviation = 2.59, sample size is 632 and z-critical for 95% confidence interval is 1.96.