Chapter 7: Sampling Distributions
(REQUIRED 7.1 and 7.2 NOTES)
Key Vocabulary:
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parameter
statistic
sampling variability
sample distribution
sampling distribution
population distribution
7.1
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margin of error
biased estimator
unbiased estimator
bias
variability
variability of a statistic
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sample proportion
sample mean
central limit theorem
What Is a Sampling Distribution?
1) What is a parameter? What is a statistic? How is one related to the other?
2) Explain the difference between  and x , between p and p̂ , between σ and sx?
3) Identify the population, parameter(with notation), sample, and statistic(with notation),:
a. The Gallup Poll asked a random sample of 515 US adults whether or not they believed in ghosts.
Of the respondents, 160 said “Yes.”
 Population
 Parameter
 Sample
 Statistic
b. A random sample of 100 female college students has a mean of 64.5 inches; which is greater than
the 63 inch mean height of all adult American women.
 Population
 Parameter
 Sample
 Statistic
4) What is sampling variability? Why do we care?
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What is the difference between variability of the parameter and sampling variability (sample
means and sample proportions)?
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How is sampling variability related to margin of error?
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Chapter 7: Sampling Distributions
(REQUIRED 7.1 and 7.2 NOTES)
5) What is the difference between the distribution of the population, the distribution of the sample, and
the sampling distribution of a sample statistic? Give an example. It is helpful to sketch graphs of
each! See graphs on pages 420-423.
 Define Population Distribution; and sketch a graph:
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Define Distribution of a sample; and sketch a graph:
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Define Sampling distribution of a statistic; and sketch a graph:
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CHECK YOUR UNDERSTANDING (page 420) complete questions 1-3
1)
2)
3)
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Chapter 7: Sampling Distributions
(REQUIRED 7.1 and 7.2 NOTES)
6) Explain the difference between these 3 distributions. Why do we care sampling distributions of a
statistics?
7) What is an unbiased estimator? What is a biased estimator? Why do we care?
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Define: Unbiased Estimator
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Explain the difference between Biased and Unbiased Estimators
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When is a statistic considered an unbiased estimator?
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CHECK YOUR UNDERSTANDING (page 426) complete questions 1-3
1)
2)
3)
3
Chapter 7: Sampling Distributions
(REQUIRED 7.1 and 7.2 NOTES)
8) What is the variability of a statistic? Why do we care?
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Define: Variability of a Statistic
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How can you reduce the variability of a statistic?
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What effect does the size of the population have on the variability (spread) of a statistic?
9) What is the difference between accuracy and precision? How does this relate to bias and variability?
10) Explain the difference between bias and variability. Sketch the 4 bull’s eyes on page 426 and clearly
explain their bias and variability.
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What is the ideal estimator?
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Chapter 7: Sampling Distributions
7.2
(REQUIRED 7.1 and 7.2 NOTES)
Sample Proportions
1) What is the difference between “p” and the sample proportion 𝑝̂ ?
2) What is the purpose of the sample proportion (“phat”) ?
3) In an SRS of size n, what is true about the sampling distribution of 𝑝̂ when the sample size n increases?
4) In an SRS of size n:
a. What is the mean of the sampling distribution of p̂ ?
b. What is the standard deviation of the sampling distribution of p̂ ? What condition must be checked?
4) What happens to the standard deviation of p̂ as the sample size n increases?
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Chapter 7: Sampling Distributions
(REQUIRED 7.1 and 7.2 NOTES)
5) When the sample size n is large, the sampling distribution of 𝑝̂ is approximately Normal. What test can
you use to determine if the sample is large enough to assume that the sampling distribution is
approximately normal? What condition must be checked?
6) CHECK YOUR UNDERSTANDING (page 437) complete questions 1-4
1)
2)
3)
4)
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