Katy had two choices of routes to get her to work. She wanted to choose the rout

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 below. A. There is not enough evidence at the 5% significance level to indicate that the average commuting times for the two routes is the same. There is not enough evidence at the 5% significance level to indicate that one route gets Katy to work faster, on average, since 0 fals within the bounds of the confidence interval B. ° 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 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.

Explanation / Answer

Here we computed the 95% confidence interval which means that the test is done at 5% level of significance. Now the confidence interval for the difference in means here is computed to be (-1, 9) which means that 0 lies inside this interval. Therefore this is not enough evidence here at the 5% level of significance that the average commuting times for the two rates are different. Therefore in other words there is no evidence here that one route is faster than the other. Therefore B is the correct answer here.

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