A researcher would like to study the relationship between average fuel economy (measured in miles per gallon) and fuel type (premium, regular unleaded, and E85). He randomly selects 90 vehicles of various
makes and models, including compact cars, full-size cars, and trucks. All of the selected vehicles have
been driven less than 6,000 miles before the experiment.
a) Does this experiment use a control group? Explain.
b) Suppose the researcher would like to use a completely randomized design. Explain how the
researcher should assign the 90 vehicles to the three fuel types.
c) An advisor to the researcher suggests using a randomized block design. Should the researcher
block on type of vehicle (compact cars, full-size cars, and trucks) or number of miles previously
driven (0–2,000 miles; 2,000–4,000 miles; and 4,000–6,000 miles)? Explain your choice of
blocking variable.

Answer and Explanation:

a. The experiment does not have a control group. This is because the control group is the one that does not have the element that will be tested. In the case of the above experiment, the element that will be tested are the three types of fuels. A control group would be a group of cars that would not receive any of the three fuels, but the experiment did not provide any information about that group.

B. The researcher must form groups of 30 vehicles, where each group will receive a specific type of fuel. As the researcher is using a random design to form these groups, we can say that the groups would be formed, without considering the type of car, where everyone would be grouped together at random.

c. The researcher must group the vehicles by the number of miles traveled, as this is an experiment in which there is no homogeneity in relation to the types of vehicles, being better, evaluate them by the distance traveled.

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