AP
®
STATISTICS
2015 SCORING COMMENTARY
© 2015 The College Board.
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Question 6
Overview
The primary goals of this question were to assess a student’s ability to (1) describe how sample data would
differ using two different sampling methods; (2) describe the sampling distribution of the sample mean for
two different sampling methods; and (3) choose the sampling method that will result in the best estimate
of the population mean.
Sample: 6A
Score: 4
In part (a) the response says no and justifies the choice by stating that “the sample will not be obtained from
the entire population of tortillas, and the tortillas that are not sampled from will tend to have a different
diameter,” satisfying the first component of section 1. In part (b) the response says Method 1 because “the
histogram is bimodal,” satisfying the second component of section 1. In part (c) the response says Method 2
because the sample is “from just one production line,” satisfying the third component of section 1. The
picture in part (c), although not required, strengthens the explanation. Because the response satisfies all
three components, section 1 was scored as essentially correct. In part (d) the response states that the
sampling distribution will be “approximately normal,” satisfying the first component of section 2. The
justification using the Central Limit Theorem is appropriate but not required. The response also correctly
identifies the mean and standard deviation of the sampling distribution of the sample mean, satisfying the
second and third components of section 2. The picture in part (d), although not required, is a nice way to
summarize the response. Because the response satisfies all three components, section 2 was scored as
essentially correct. In part (e) the response says Method 1 and correctly describes the sampling distribution
of the sample mean for Method 2 as having some means close to 5.9 and other means close to 6.1, satisfying
the first component of section 3. The picture in part (e), although not required, strengthens the already
correct explanation. In part (f) the response says Method 1 because on a single day, “Method 2 is likely to
produce a sample mean close to either 5.9 inches or 6.1 inches” while the average for Method 1 will be “very
close to 6.0 inches.” Because the response satisfies both components, section 3 was scored as essentially
correct. Because all three sections were scored as essentially correct, the response earned a score of 4.
Sample: 6B
Score: 3
In part (a) the response says “Method 2 will not produce a sample that is representative of the population”
because “only 1 of the 2 production lines is selected,” satisfying the first component of section 1. In part (b)
the response says Method 1 because the histogram “displays 2 apparent peaks,” satisfying the second
component of section 1. In part (c) the response says Method 2 because the sample comes from “only one of
the production lines,” satisfying the third component of section 1. Because the response satisfies all three
components, section 1 was scored as essentially correct. In part (d) the response correctly identifies the mean
and standard deviation of the sampling distribution of the sample mean, satisfying the second and third
components of section 2. The response also states that the sampling distribution “will be normally
distributed,” satisfying the first component of section 2. It would have been better if the response said the
distribution should be approximately normally distributed, but in the scope of a six-part investigative task,
this was considered a minor error. Because the response satisfies all three components, section 2 was scored
as essentially correct. In part (e) the response says Method 2, which is incorrect. It appears that the response
is describing the distribution of sample data from Method 2, as in part (c), rather than the sampling
distribution of the sample mean. In part (f) the response says Method 1 and argues that on a single day,
Method 1 would produce a mean “at about 6 in.” while Method 2 would likely “provide a sample mean closer
to 5.9 in. or to 6.1 in.,” satisfying the second component of section 3. Because the response satisfies only one