Problem 2: The standard course at a local defensive-driving school includes several films depicting violent car crashes and graphic pictures of injuries sustained in these crashes. The driving school has shown these videos for many years, believing that they reduce the students' average speeds on the highway. A group of concerned citizens, who feel that these videos are very disturbing, is not convinced that the videos reduce highway speeds enough to make a significant difference in highway safety. In fact, the group claims that these videos Reduce a person's speed on the highway by less than 5 miles per hour, on average. To test the claim, the citizens install electronic data recorders (EDRs) on the vehicles of 10 volunteers, who agree to drive as they would normally for two weeks while the EDR records their vehicles' speeds. After the initial driving period, each volunteer watches the videos. Then the EDRs again record their vehicles' speeds for/nanother two weeks. The following table contains the average highway speeds for each volunteer for the two-week periods before and after watching the videos. Average Highway Speeds (in Miles per Hour) Before After 75.83 72.13 80.12 73.87 65.41 66.09 70.03 68.43 73.91 71.45 76.02 73.67 75.10 70.19 67.89 65.34 81.12 75.31 77.67 70.92 Use these data to test the concerned citizens' claim that these videos reduce a person's speed on the highway by less than 5 miles per hour, on average. Use a 0.05 level of significance. Assume the paired differences are normally distributed.

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