Practise identifying the largest population supported by a study, using its sampling frame and selection method to justify or limit any statistical generalization.
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.
After the investigation was completed, James verified that the conditions for inference were met and conducted a hypothesis test. He discovered the mean mileage when using the autopilot feature was significantly higher than the mean mileage when not using the autopilot feature.
James is a member of a Model D club with thousands of members who all drive Model D cars. He will give a presentation at a Model D club members' meeting later this year and would like to state that the results of his hypothesis test apply to all Model D cars in his club. Another member of the club who is a statistician tells James his findings do not apply to all Model D cars in the club. What change would James need to make to his original study to be able to generalize to all Model D cars in the club?
In order to generalize his findings to all Model D
cars in his club, he would need to randomly select Model D cars from the club. He would then need to carry out a similar study using the
Model D cars that were randomly sampled from the club.
Essentially correct (E) if the response satisfies the following three components:
1. The response indicates that more cars must be sampled
2. The response indicates that random sampling is required for generalization
3. The response is in context, which would
include sampling from the population of
interest (Model D cars from his club)
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:
- Component 3 may be satisfied by using "members" of the club or "owners" in the club rather than cars.
- Any discussion of experimental design beyond the sample selection (such as conditions or two-sample design) should be ignored.