Example 1: The owner of a local restaurant chain in town was trying to determine the best location to open her next restaurant and she had narrowed it down to two locations. She wanted to make her decision based on how interested residents in each area were in her restaurant. So she hired an independent company to survey residents from each neighborhood to gauge their interest. In the first neighborhood, 120 residents were surveyed and 84 of them expressed interest in the new restaurant. In the second neighborhood, 200 residents were surveyed and 110 of them expressed interest in the new restaurant. Carry out an appropriate hypothesis test at the =0.02 level to determine if there is sufficient evidence to suggest that one neighborhood is more interested in the new restaurant than the other.

Example 2: Bryan coaches track and field at a local high school and during the previous season he got the impression that his 800m runners performed better when their races were in the morning as opposed to the afternoon. This season, he wanted to determine if his runners in fact performed better in the morning so he recorded all of their times for each race throughout the entire season. The data that he recorded for the morning and afternoon races are shown below. Carry out an appropriate hypothesis test at the =0.05 level to determine if his 800m runners performed better in the morning than in the afternoon. Sample Size Standard Deviation Average Morning 38 14 122 Afternoon 54 13 124 Example 3: Alexis has a lengthy commute to work each day. There are two main routes that she takes on her way to work and they both average 40 minutes. Alexis likes to be able to predict how long before work she needs to leave in order to make it on time, and since both routes take the same average amount of time, she was interested in determining whether or not one route was more consistent with its timing. So she recorded how long it took her to drive to work 20 times total (Data shown below). Carry out an appropriate hypothesis test at the =0.05 level to determine if one route yields more consistent times than the other. Route 1 41 42 41.5 40.5 41 40.5 40 39 40 42 Route 2 37 36 39 38 37 40 44 41 43 38 Standard Deviation Sample Size Route 1 0.950 10 Route 2 2.669 10