Section 7.1
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• A parameter is a number that describes some
characteristic of the population. In statistical practice, the
value of the parameter is usually not known because we
cannot examine the entire population.
• 𝜇 𝑎𝑛𝑑 𝜎
• A statistic is a number that describes some characteristics
of a sample. The value of a statistic can be computed
directly from the sample data. We often use a statistic to
estimate an unknown parameter.
• 𝑥 𝑎𝑛𝑑 𝑆𝑥
Parameter v. Statistic
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• For the sample of 54,100 households contacted by the
CPS, the mean income was 𝑥 = $68,424.
• Statistic –
• Parameter –
Example
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• The value of a statistic varies in repeated random
sampling.
• We will do a penny activity on Monday 
Sampling Variability
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• Take a large number of samples from the same
population.
• Calculate the statistic for each sample.
• Make a graph of the values of the statistic.
• Examine the distribution displayed in the graph for
SOCS.
What would happen if we
took many samples?
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• The sampling distribution of a statistic is the
distribution of the values taken by the statistic in all
possible samples of the same size from the same
population.
Sampling Distribution
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• The population distribution give the values of the
variable for all the individuals in the population.
• If we would have combined all of the data before finding
the mean of our pennies and put them all on one dotplot,
we would have made a population distribution.
Population Distribution
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• Don’t confuse the sampling distribution with a
distribution of sample data, which gives the values of the
variable for all individuals in a sample.
• Example –
• In your groups you made distributions of sample data.
• As a class, we made a sampling distribution.
• If we had all of the years of all pennies, that would be a
population distribution.
Be careful!
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• A statistic used to estimate a parameter is an unbiased
estimator or a biased estimator. Bias means that the
center (mean) of the sampling distribution is not equal to
the true value of the parameter.
• It is called “unbiased” because in repeated samples, the
estimates won’t consistently be too high or too low. It
doesn’t mean it will be perfect!
Describing Sampling
Distributions
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• The variability of a statistic is described by the spread
of its sampling distribution.
• The spread of the sampling distribution does not depend
on the size of the population, as long as the population is
at least 10 times larger than the sample.
• Larger samples give smaller spread.
Variability of a Statistic
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• When trying to estimate a parameter, choose a statistic
with low or no bias and minimum variability.
• Don’t forget to look at shape of the sampling distribution
before doing inference.
Extra Stuff!
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• Pg 428 (5, 6)
• Pg 439 (31, 36)
• Pg 459 (54, 56)
Homework
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