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# 8.3 The Sampling Distribution of a Sample Proportion

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## Jaime Pitman

on 9 April 2014

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#### Transcript of 8.3 The Sampling Distribution of a Sample Proportion

8.3 The Sampling Distribution of a Sample Proportion
The objective of many statistical investigations is to draw a conclusion about the proportion of individuals or objects in a population that possess a specified property.
For example, coffee drinkers who regularly drink decaffeinated coffee
NEW NOTATION!
Let's EXPERIMENT!!
We're each going to flip a coin 20 times. Then calculate the proportion and plot on the dotplot.
What if...

What if we flipped the coins 50 times and found the proportion of heads?
Sampling Distributions of p
Sampling Distributions of p depends on both:
n, sample size
, proportion of successes in the population
Properties of Sampling Distribution of p
The mean value of the sampling distribution p is equal to the proportion of successes in the population.
Holds true when no more than 10% of the population is included in the sample
When n is large and is not too near 0 or 1, the sampling distribution of p is approximately normal.
RULE #1
RULE #2
RULE #3
Center
Shape
Conditions on Shape (Rule #3)
The sampling distribution of p can be considered a normal distribution if:
EXAMPLE
What is the probability that the proportion of defective products in the sample is greater than 0.10? P (z > .10)