Question

Katy had two choices of routes to get her to work. She wanted to choose the route that would get her to work fastest, on average. To determine which route would get her to work faster, on average, she randomly selected 10 days and took Route 1 on those 10 days. Then she randomly selected a different 10 days and took Route 2 on those 10 days. She recorded the time, in minutes, it took her to get from her house to work on each of those 20 days. From her data, she constructed the 95% confidence interval for the difference in mean commuting times (Route 1-Route 2) in minutes as (-1,9) Based on this confidence interval, which of the following is a correct statement? Choose the correct answer belowA. There is evidence at the 5% significance level to indicate that one route gets Katy to work faster, on average, since one bound is close to 0. B. There is not enough evidence at the 5% significance level to indicate that the average commuting times for the two routes is the same.C. There is evidence at the 5% significance level to indicate that one route gets Katy to work faster, on average, since 0 falls between the bounds of the confidence interval.D. There is not enough evidence at the 5% significance level to indicate that one route gets Katy to work faster, on average, since 0 falls within the bounds of the confidence interval.

Answer 1

Answer:

D. There is not enough evidence at the 5% significance level to indicate that one route gets Katy to work faster, on average, since 0 falls within the bounds of the confidence interval.

Step-by-step explanation:

At 5% confidence level, Katy found difference in mean commuting times (Route 1-Route 2) in minutes as (-1,9).

Since no difference in means (0 min) falls within the confidence level (-1,9), we can not reject the hypothesis that there is no difference in mean commuting times when using Route1 or Route2.

A higher significance level(10% etc) may lead a shorter confidence interval leaving 0 outside and may reach a conclusion that Route1 takes longer than Route2