A highway department is trying to convince motorists to take a new commute route to work by claiming that the new route will take the same amount of time, on average, as the old route. To test this claim, a group of eight motorists commuted using the new route on one day and the old route on another day. The commute time results are shown below (in minutes). Based on these results, a 95% confidence interval for the (population) mean difference is 0.16 minutes to 2.47 minutes. Assuming the data have a normal distribution, specify whether each of the following conclusions is correct or incorrect.
A. With 95% confidence, there is a significant difference between the mean commute times for the new route and the old route.
B. With 95% confidence, the mean commute time for the new route is lower than the old route.
C. With 95% confidence, the mean commute time for the new route is higher than the old route.
D. With 95% confidence, there is no significant difference between the mean commute times for the new route and the old route.
A. With 95% confidence, there is a significant difference between the mean commute times for the new route and the old route.
C. With 95% confidence, the mean commute time for the new route is higher than the old route.
Since the 95% confidence interval does not contain zero, this implies there is a significant difference between the mean commute times for the new route and the old route with 95% confidence. Moreover, since the sample difference is positive, this implies that the mean commute time for the new route is higher than the old route with 95% confidence. The remaining answer choices are incorrect.
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