AP
®
STATISTICS
2011 SCORING COMMENTARY
Question 3
Overview
The primary goals
of this question were to assess students’ ability to (1) describe a process for
implementing cluster sampling; (2) describe a statistical advantage of stratified sampling over cluster
sampling in a particular situation.
Sample: 3A
Score:
4
In part (a) the st
udent assigns each floor a unique number, 1–9, and correctly describes the use of a
random number generator to select two floors, including what to do in the case of repeated random
numbers. The student then indicates that all eight apartments on the selected floors will be carpeted.
Part (a) was scored as essentially correct. In part (b) the student begins by stating that for cluster
sampling “it is possible that no apartments with kids would be selected,” and gives the combinations of
two floors for which this statement is true. The student argues that this is “bad … because kids tend to
wear out carpets more than adults,” and provides a consequence of such a sample for the owner. The
student then states that a “stratified sample would work better” because the sample will contain
“apartments with and without children.” The strong response in this part was scored as essentially
correct. Because both parts were scored as essentially correct, the response earned a score of 4.
Sample: 3B
Score:
3
In part (a) the st
udent suggests that one “could randomly select 2 floors to carpet.” Although this does
not explicitly state that eight apartments are to be carpeted, the idea of carpeting entire floors is
sufficient to indicate that four apartments on each floor will be carpeted. However, the student makes
no attempt to implement a valid random sampling procedure for selecting the two floors. Part (a) was
scored as partially correct. In part (b) the student indicates that the “advantage to this [the stratified
sample] would be to see if kids play a big role in the carpets [sic] wear,” as opposed to the cluster
sample in which “you might not get any kids.” The communication is weak, but the student does
address the difference in carpet wear between the apartments with and without children and also
indicates that a cluster sample might not include apartments with children. Part (b) was scored as
essentially correct. Because one part was scored as essentially correct and one part was scored as
partially correct, the response earned a score of 3.
Sample: 3C
Score:
2
In part (a) the student describes a non-cluster sample and does not describe a random sample of two
fl
oors from the nine. Part (a) was scored as incorrect. In part (b) the student indicates in the first two
sentences that a stratified sample will have apartments with and without children (as opposed to the
cluster sampling method) and that “you get to see how the carpet wears” in both types of apartments.
This is sufficient to answer the question; the remaining sentences were considered extraneous and did
not detract from the response. Part (b) was scored as essentially correct. Because one part was scored as
essentially correct and one part was scored as incorrect, the response earned a score of 2.
© 2011 The College Board.
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