1. Chapter 18 – Sampling Distribution Models

2. How accurate is our sample?
Sometimes different polls show different results for the same question.
Since each poll samples a different group of people, we should expect some variation in the results.
We could try drawing lots of samples and looking at the variation amongst those samples.

3. Coin flipping experiment
Open up the web page:
Flip 10 coins and record the number of heads
Flip 50 coins and record the number of heads
Flip 100 coins and record the number of heads
Let’s look at a histogram with your results

4. Sampling Distribution Model for a Proportion
Our histogram of the sample proportions started to look like a Normal model
The larger our sample size gets, the better the Normal model works
Assumptions:
Independence: sampled values must be independent of each other
Sample Size: n must be large enough

5. Conditions to check for assumptions
Randomization Condition:
Experiments should have treatments randomly assigned
Survey samples should be a simple random sample or representative, unbiased sample otherwise
10% Condition:
Sample size n must be no more than 10% of population
Success/Failure Condition:
Sample size needs to be large enough to expect at least 10 successes and 10 failures

6. Sampling Distribution Model for a Proportion
If the sampled values are independent and the sample size is large enough,
The sampling distribution model of is modeled by a Normal model with:

7. Example based on our coin flips
10 coins 50 coins coins
Mean =
SD =

8. Model of 100 coin flips

9. Example: Proportion of Vegetarians
7% of the US population is estimated to be vegetarian. If a random sample of 200 people resulted in 20 people reporting themselves as vegetarians, is this an unusually high proportion?
Conditions:
Randomization
10% condition
Success/Failure

10. Vegetarians Example continued
Since our conditions were met, it’s ok to use a Normal model.
= 20/200 = .10
E( ) = p = .07
z = This result is within 2 sd’s of mean, so not unusual

11. 68-95-99.7 Rule with Vegetarians
68%
95%
98%
-3σ
-2σ
-1σ p 1σ 2σ 3σ

12. More with vegetarians
What is the probability that we get a random sample of 200 people with 10% vegetarians?