The document discusses sampling distributions and standard error. It contains examples of sampling distributions for statistics graduate program enrollment and sample means from different populations. It explains that standard error measures how much a statistic varies from sample to sample. Standard error is higher for distributions with more variability and for those based on smaller sample sizes, as smaller samples are more sensitive to outliers.

1. Section 3.1
Sampling
Distributions
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2. The sampling distribution is shown for enrollment in
statistics grad schools. One dot represents:
A. Enrollment at one statistics grad program
B. One sample mean
C. 1000 different enrollments
D. 1000 sample means
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3. The sampling distribution is shown for enrollment in
statistics grad schools. The population parameter is
closest to:
A. 5
B. 10
C. 20
D. 55
E. 65
The distribution appears to be centered at
about 55.
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4. The sampling distribution is shown for enrollment in
statistics grad schools. The standard error is closest to:
A. 5
B. 10
C. 20
D. 55
E. 65
The middle 95% of the data appears to
extend about 20 out on either side from the
center.
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5. Random samples are taken from a population
with mean , and the sample means are shown in
the dotplots below. We estimate that is about
A. 5
B. 10
C. 15
D. 25 E. 200
The distributions appear to be centered at
about 25.
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6. One set of sample means below was computed
using sample sizes of n = 50 and the other was
computed using sample sizes of n = 200. We have:
A. n = 50 for C1 and n = 200 for C2
B. n = 200 for C1 and n = 50 for C2
C. It is impossible to tell from the information given.
The variability goes down as the sample
size goes up.
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7. The standard error for the sampling
distribution given in C2 is about:
A. 5 B. 10
C. 15
D. 25
E. 30
The middle 95% of the distribution appears to
extend about 10 on either side of the center.
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8. The standard error for the sampling
distribution given in C1 is about:
A. 1
B. 2
C. 5
D. 10
E. 25
The middle 95% of the distribution appears
to entend about 2 on either side of the
center.
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9. Standard Error
The more the statistic varies from sample to
sample, the
a) higher
b) lower
the standard error.
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The standard error
measures how much the
statistic varies from sample
to sample.
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10. Reese’s Pieces
Sampling Distribution:
a) 0.05
b) 0.15
c) 0.25
d) 0.35
Middle 95%: 0.2 to 0.7
=> SE 0.5/4 = 0.15
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11. Sample Size
Suppose we were to take samples of size 10 and
samples of size 100 from the same
population, and compute the sample means.
Which sample mean would have the higher
standard error?
a) The sample means using n = 10
b) The sample means using n = 100
Smaller sample sizes give more
variability, so a higher standard error
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