1. Sampling Distributions
Section 9.1.1
Lesson 9.1.1

2. Starter 9.1.1
Write a paragraph that explains the differences between 3 types of random samples:
Simple Random Sample
Systematic Random Sample
Stratified Random Sample

3. Today’s Objectives
Students should be able to describe the difference between a parameter and a statistic.
Students should be able to define a sample mean and a sample proportion.
Students should be able to define and describe a sampling distribution.
California Standard 15.0
Students are familiar with the notions of a statistic of a distribution of values, of the sampling distribution of a statistic, and of the variability of a statistic.

4. Parameters and Statistics
A parameter is the value of a variable that describes some characteristic of interest about a population.
The basic objective in data analysis is to estimate a population parameter.
Numeric variable: find mean μ and std dev σ
Categorical variable: find proportion p
A statistic is the value of a variable that describes some characteristic of interest about a sample drawn from a population.
The technique of estimation is to study a random sample of the population to get a statistic.
Numeric variable: mean and std dev s
Categorical variable: proportion

5. Example
In the presidential election of 2000 in Florida, the Gore-Bush results were so evenly divided that we could have just flipped coins.
Let’s try to estimate the true proportion of Florida voters who supported Bush by simulating a random sample of 20 voters.
The result will be a sample statistic
We will then combine results to get a sampling distribution.

6. Activity
Toss a coin 20 times and record the proportion of heads obtained.
This is a sample proportion
If we had used a numeric variable (like: the number of coins in each students‘ pockets) it would be a sample mean
Simulate another 9 trials on the calculator and write the 9 proportions on paper.
randBin(20,.5,9)/20 is a quick way to do it
Post your results as a dotplot on the board with other students’ results.
Note that results differed: this is sampling variability
The dot plot created shows a sampling distribution
Sketch and describe the class distribution on paper.

7. Four Questions:
What is the difference between a parameter and a statistic?
A parameter is the value (usually unknown) of a variable of interest for a population.
A statistic is the measured value (and therefore known) of that variable for a sample drawn from the population.
What is a sample proportion?
A sample proportion is the calculated proportion of a categorical variable from one sample of a population.
What is a sample mean?
A sample mean is the calculated mean of a numeric variable from one sample of a population.
What is a sampling distribution?
A sampling distribution shows the distribution of many sample statistics (p-hat or x-bar) taken from a population.
In theory, it is the distribution of all possible samples that could be taken
Like any distribution, it has a center, shape and spread.

8. Today’s Objectives
Students should be able to describe the difference between a parameter and a statistic.
Students should be able to define a sample mean and a sample proportion.
Students should be able to define and describe a sampling distribution.
California Standard 15.0
Students are familiar with the notions of a statistic of a distribution of values, of the sampling distribution of a statistic, and of the variability of a statistic.

9. Homework
Read pages 454 – 459
Do problems 1 – 4, 6