#### 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

Spread

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)

**Practice on Your Own!**

Suppose 3%, or 𝜋=0.03, of the people contacted by phone are receptive to a certain sales pitch and buy your product. A sample size of 2,000 is considered.

1) Show that this sample size is large enough to justify using the normal approximation to the sampling distribution of 𝑝.

2) What is the mean of the sampling distribution of 𝑝?

3) What is the standard deviation of the sampling distribution of 𝑝?

4) What is the probability that the proportion of people who are receptive to the sales pitch is less than 0.025? P( z < .025)

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