Transcript Section 9.1 Sampling Distributions

Section 7.1
Sampling Distributions
Vocabulary Lesson
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Parameter
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A number that describes the population.
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This number is fixed. In reality, we do not know its
value because we can’t examine the WHOLE
population.
Statistic
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A number that describes a sample.
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We know this value because we compute it from our
sample, but it can change from sample to sample.
We use a statistic to estimate the value of a
parameter.
Helpful hints
– Statistic
Population – Parameter
Sample
Notation
Parameter
Mean
Standard
Deviation
Proportion
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Statistic
x

s
p
p̂
Example
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What is the mean income of households in the
United States?
The government’s Current Population Survey
contacted a sample of 50,000 households in 2000.
The mean income of this sample was $57,045.
What is the parameter of interest?
Is $57,045 a parameter or a statistic?
If we took another sample of 50,000 households,
would μ change? What about x ?
Example 2
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A carload of ball bearings has mean diameter
2.5003 cm. This is within the specifications
for acceptance of the lot by the purchaser.
By chance, an inspector chooses 100
bearings from the lot that have mean
diameter 2.5009 cm. Because this is outside
the specified limits, the lot is mistakenly
rejected.
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State whether the highlighted numbers are
parameters or statistics. Use correct notation.
What is the population?
Sampling Variability
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If we took repeated samples of the
households in the United States, each one
would likely produce a different sample
mean.
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That’s called sampling variability:
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The value of a statistic varies in repeated random
sampling.
What would happen if we took
many samples?
If you are conducting a simulation, you should:
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Take a large number of samples from the same
population.
Calculate the sample mean or sample proportion
for each sample.
Make a histogram of the values of x-bar or p-hat.
Examine the distribution displayed in the
histogram for shape, center, and spread.
Revisiting IQ
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Let’s simulate taking a random sample size
25 from a normal population (100,15). We’ll
calculate the sample mean for each sample
and record the result. We’ll repeat this 20
times. We could, but we aren’t!
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We’ve would have found the sampling
distribution.
 The sampling distribution of a statistic is the
distribution of values taken by the statistic in
all possible samples of the same size from
the same population.
Homework
Chapter 7
#1-4, 5-8, 18, 19