Students can bike to a park on the other side of a lake by going around one side of the lake or the other. After much discussion about which was faster, they decided to perform an experiment. Among the 12 students available, 6 were randomly selected to follow Path A on one side of the lake and the rest followed Path B on the other side. They all went on different days so the conclusion would apply to a variety of conditions.

(a) Is there a significant difference between the mean travel times between the two paths? State the assumptions you have made in performing the test.
(b) Suggest an alternative design for this study that would make the comparison more effective.

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Travel Time (minutes) Path A 10 12 15 1 16 1 Path B12 15 17 13 18 16