# Can we conclude, at the 0.05 level of significance, that the mean travel times of the two routes are different?

## Amy has two ways to travel from her home in Norco to her office in Los Angeles. One is to go via the 10 Freeway, and the other is to go via 60 Freeway. In order to determine which way she should travel on a daily basis, Amy has recorded the travel times for samples of twelve trips via the 10 Freeway and twelve trips via the 60 Freeway. The following table gives the travel times (in minutes) for the twenty-four trips: Travel times in minutes 10 Freeway 72,70,71,71,70,73,74,70,73,68,73,71 60 Freeway 75,68,73,71,67,76,76,75,75,75,69,71 Assume that the two populations of travel times are normally distributed and that the population variances are equal.

We cannot conclude that the travel times on the two freeways are different at the $0.05$ significance level.
Plug the data sets into two different lists in your graphing calculator. Then go the tests and choose the 2 sample t-test. For the symbol, use $\ne$. Their population variances are equal so the result should be pooled. Then click draw:
Your p-value should come out to be $.2529$. Since $.2529 > .05$, we cannot conclude that the travel times on the two freeways are different at the $0.05$ significance level.