AP Statistics 1.13 Experimental Designs

A car maker produces four different models of cars: A, B, C, and D. A group of researchers is investigating which model of car has the longest distance traveled per gallon of gas (mileage). Higher mileage is considered better than lower mileage. The researchers will conduct a study in which they contact several owners of each model of car and ask them to estimate their mileage.

Model D has an autopilot feature, in which the car controls its own motion with human supervision. James owns a Model D car and will investigate whether using the autopilot feature results in higher mileage than not using the autopilot. James will drive his car on 70 different days to and from work, using the same route at the same time each day. James will record the mileage each day.

James will use a completely randomized design to conduct his investigation. Describe an appropriate method James could use to randomly assign the two treatments, driving using the autopilot feature and driving without using the autopilot feature, to 35 days each.

Number the days in the experiment from 1 to 70. Using a random number generator, generate 35 unique integers from 1 to 70, inclusive. Assign the days with those 35 unique integers for James to drive the car with autopilot and assign the remaining 35 days for James to drive the car without autopilot.
(Alternative solution)

Using 70 equally sized slips of paper, label 35 "with autopilot" and 35 "without autopilot." Mix the slips of paper in a bag. Each day for the 70 days, select a slip of paper (without replacement) to determine the driving method for that day.

Scoring

Essentially correct (E) if the response satisfies the following three components:

Creates appropriate labels for the units/treatments

Describes how to correctly implement the random process so that every possible random assignment is equally likely

The response indicates a random process that results in 35 days assigned to using autopilot and 35 days assigned to not using autopilot

Partially correct (P) if the response satisfies only two of the three components required for E.

Incorrect (I) if the response does not meet the criteria for E or P.

Additional Notes:

- For responses that use slips of paper (or marbles or equivalent) to represent treatments

To satisfy component 1 some slips must be labeled or assigned to represent autopilot and some labeled or assigned to represent no autopilot (e.g., blue marbles represent autopilot and yellow marbles represent no autopilot).

To satisfy component 2 the slips of paper must be mixed/shuffled, and the response must clearly link the treatment selected to a day (e.g., each day James selects a slip to determine the driving method).

To satisfy component 3 the response must indicate that there are 35 slips (or marbles of a specific color) for each treatment and the response must indicate that slips of paper (marbles) are selected without replacement.

- For responses that use slips of paper labeled from 1 to 70 (or an equivalent interval)

To satisfy component 1 the days must be labeled 1 to 70.

To satisfy component 2 the slips of paper must be mixed/shuffled, and the response must clearly link the day number selected to autopilot or no autopilot.

To satisfy component 3 the response must indicate that slips of paper are selected without replacement and that 35 days are assigned to each treatment.

- For responses that use a random number generator with days labeled from 1 to 70 (or an equivalent interval)

To satisfy component 1 the days must be labeled 1 to 70.

To satisfy component 2 the response indicates that the random number generator selects numbers 1 to 70 inclusive, and the response clearly links the day number selected to autopilot or no autopilot.

To satisfy component 3 the response must indicate that numbers are selected without repeats and that 35 days are assigned to each treatment.

- For responses that flip a coin for each day (or roll a die and note odd/even, generate a random number 1 or 2, or equivalent)

To satisfy component 1 each outcome must be linked to a treatment (e.g., heads equals autopilot, tails equals no autopilot).

To satisfy component 2 the response must clearly link the outcome of the coin flip to a day (e.g., each day James flips a coin to determine the driving method). Note: If the response includes a stopping rule (e.g., when 35 days are assigned one treatment, the remaining days are assigned the other treatment), component 2 is not satisfied because this plan increases the probability that the last days will have the same treatment, which does not meet the equally likely random assignment requirement.

To satisfy component 3 the response must indicate that 35 days are assigned to each treatment using a stopping rule. If there is no stopping rule, component 3 is not satisfied.

- If a response uses a random number generator or slips of paper with the numbers 1 to 70 and does not initially number the days from 1 to 70, component 1 may be satisfied if the response indicates a link between the number selected and the day (e.g., if 3 is selected, James uses autopilot on the third day).

- Responses that do not use any random process should be scored I. For example, "number the days from 1 to 70 and use autopilot on odd-numbered days."

- Responses that use blocking do not satisfy component 2 because all possible random assignments are not equally likely.

- If the response describes two ways to perform the random assignment, assign the score for the weaker assignment process.

1.13.B—Identify experimental designs question 1