Download Sampling Distribution of - Fort Thomas Independent Schools

AP Statistics
Notes
Name: ____________
Date: _____________
Lesson 9.2: The Sampling Distribution of
the Sample Proportion, p̂
Learning Targets:
F: Recognize when a problem involves a sample proportion, p̂ .
G: Find the mean and standard deviation for the sampling distribution of a sample proportion p̂ for an SRS of
size n from a population having population proportion p.
H: Know that the standard deviation (spread) of the sampling distribution of p̂ gets smaller at the rate
n as
the sample size n gets larger.
I: Recognize when you can use the Normal approximation to sampling distribution of p̂ .
J: Use the Normal approximation to the sampling distribution of p̂ to calculate probabilities that concern p̂ .
Vocabulary:
sampling distribution of sample proportion p̂
mean and standard deviation of sampling distr. of p̂
1.
Sampling Distribution of the Sample Proportion, p̂
Population
Have a large population with population
proportion, p, having some characteristic
of interest.
Sampling Distribution of p̂
Mean:  p̂ = p
Standard Deviation:  p̂ =
p(1  p)
n
This formula for standard deviation of p̂
only works when the population is at least
10 times as large as the sample.
Sample
Choose a SRS of size n from this
population.
Sample proportion, p̂ , have the
characteristic of interest.
Sampling Distribution of p̂
Approximately Normal ?
The sampling distribution of p̂ is
approximately normal if
np  10
and
n(1-p)  10
2.
Example Problem
The Gallup Poll once asked a random sample of 1540 adults, “Do you happen to
jog?” Suppose that in fact, 15% of all adults jog. Find the probability that
between 13% and 17% of the sample jog.
Population:
Sample:
Sampling Distribution of p̂ :
Sampling Distribution of p̂
Approximately Normal ?:
Calculate Probabilities:
Interpret Results:
Find this probability for SRS’s of sizes 200, 800, and 3200.
What general conclusion can you draw from your calculations?