1. Section 7.3

2. Use sample proportions when you are interested in categorical variables, expressed as proportions.
Ex: What proportion of high school students watch YouTube more than regular TV?
Use sample means when you are interested in quantitative variables.
Ex: What is the mean SAT score of US high school seniors?

3. Take a sample of 25 pennies and calculate the mean and standard deviation of their years.
Put your statistics on the charts.

4. Sampling Distribution Review
Keep taking samples of size n from a population with mean μ.
Find the sample mean x for each sample.
Collect all the x's and display the distribution.

5. The Sampling Distribution of the Sample Mean, x
Compare the shape, center and spread of each of the following. What do you notice?

6. The Sampling Distribution of the Sample Mean, x
The sampling distribution of the sample mean is centered at the population mean µ and is less spread out than the population distribution.
as long as the 10% condition is satisfied: n ≤ (1/10)N.

7. Think about it....as n, the sample size, increases, the standard deviation of the sampling distribution of x decreases.
To cut the standard deviation in half, how much do you need to increase the sample size?

8. See alternative example in Ch. 7 Notes

9. Sampling from a Normal Population
The shape of the distribution of depends on the shape of the population distribution.
When the population distribution is Normal, the sampling distribution of will also be Normal.
This is true regardless of sample size as long as the 10% condition is met.

10. Online Statbook Sampling Distribution Applet
Pay attention to the values of each number.

11. REMARKABLE!! The Central Limit Theorem
Fact: Most population distributions are NOT Normal.
BUT: as the sample size increases, the distribution of the sample mean x changes shape to become more Normal.
When the SRS size n from any population is large, the sampling distribution of the sample mean is approximately Normal.

12. How small is small and how large is large?
It depends on the population distribution. If it is far from normal, n must be large. If this is unknown, then n must be large.
The CTL says that if the population is unknown or not Normal, the sampling distribution of will be approximately Normal if n ≥ 30.

14. Central Limit Theorem:
If the population distribution is
Normal
Not Normal

16. Complete Building Better Batteries Case Closed on p. 460 - 461