Question

A man who moves to a new city sees that there are two routes he could take to work. A neighbor who has lived there a long time tells him Route A will average 5 minutes faster than Route B. The man decides to experiment. Each day he flips a coin to determine which way to​ go, driving each route 10 days. He finds that Route A takes an average of 42 ​minutes, with standard deviation 11 minutes and Route B takes an average of 47 minutes, with standard deviation 55 minutes .

Histograms of travel times for the routes are roughly symmetric and show no outliers. Complete parts a and b. Use

alphaαequals=0.05.

​a) Find a​ 95% confidence interval for the difference between the Route B and Route A commuting​ times

How can the degree of freedom be found using the table?

Answer 1

Since histograms of travel times for the routes are roughly symmetric and show no outliers, we can assume population distribution as normal.