1
Chapter 18a (Sampling Distribution Models for Proportions)
Note:
For now, we will just address sampling distributions in the context of proportion settings.
With exam 4, we will come back to chapter 18b for sampling distributions of sample means (pg. 466476)
Activity 1
Suppose we wish to predict the percentage of all U.S. teenagers whose favorite type of cookie is a
chocolate chip cookie.
Let’s define a success as a teenager whose favorite cookie is chocolate chip, and a
failure as a teenager whose favorite is any other kind.
To make our prediction, we poll a random sample of
500 U.S. teens regarding their preferences, and find that 280 favor chocolate chip.
The parameter of interest we want to predict is
p
(the proportion of successes in the entire population).
We will use the proportion of successes in our sample
^
p
to make our prediction.
A. What is the proportion of successes in this random sample of n = 500 teens?
^
p
=
B. Suppose a second random sample of n = 500 teens is surveyed.
Do you expect this second random
sample to yield the same proportion of successes as the first sample?
Why or why not?
Note that we use the
sample statistic
^
p
to represent the proportion of successes in a sample and the
parameter
p
to represent the proportion of successes in the entire population.
Usually, the value of the
population parameter (
p
,
μ
,
σ
) is unknown.
In this case, the only way to know the true value of
p
is
to poll every U.S. teen on their cookie preferences.
This type of polling is called a census, and is very
timeconsuming and costly.
Assuming the sample data is unbiased (representative of the entire
population), the sample statistic (
^
p
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 Spring '08
 Ripol
 Statistics, Normal Distribution, Standard Deviation, Variance, Probability theory, Binomial distribution

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