The police department of a large city uses conventional gasoline for its fleet of police cars. For environmental reasons, the mayor wants to switch to a mixture of gasoline and ethanol. But the police commissioner objects to this plan, because he believes that it will decrease fuel efficiency and strain the departments budget. They decide to conduct an experiment to estimate the effects of ethanol on fuel efficiency. A consultant proposes two different designs.

Design 1: 100 police officers are randomly divided into 5 groups of 20. Each officer is given a car to drive for a 12-hour shift. For Group 1, no ethanol (0%) is added to the fuel. For Groups 2, 3, 4, and 5, the levels of ethanol are 2.5%, 5%, 7.5% and 10%, respectively. The response variable is fuel efficiency, measured in miles per gallon.

Design 2: 20 police officers are given cars to drive, and each officer drives the same car for 5 consecutive 12-hour shifts. Each officer drives for one shift at each level of ethanol (0%, 2.5%, 5%, 7.5%, 10%). For each officer, the 5 levels of ethanol are given in random order. The response variable is fuel efficiency, measured in miles per gallon.

1. What kind of experimental design is Design 1? (2 points)
2. What kind of experimental design is Design 2? (2 points)
3. The mayor says, Design 1 will obviously give more accurate results, because the sample size is larger. Design 1 uses 100 officers, but Design 2 uses only 20. The police commissioner says, The two designs will be equally accurate, because each design uses 100 shifts. Is the mayor correct? Why? (2 points)
4. Is the police commissioner correct? Why? (2 points)
5. Which design do you think will give more accurate estimates of treatment effects? (What will determine whether Design 1 or Design 2 is better?) Why? (2 points)