SWBAT (students will be able to): Define/recognize/use/describe the following: 

• Parameter vs. Statistic
• Sampling Distribution
• Distribution of a Sample
• Distribution of a Population

SWBAT Evaluate claims using sampling distributions

A statistic is a number that describes some characteristic of a sample.

A parameter is a number that describes some characteristic of a population. 

The table below shows three commonly used statistics and their corresponding parameters. These symbols are widely used in statistics and you are expected to know and use these symbols and terms. The symbol for sample mean is read "x bar" and the symbol for sample proportion is read "p hat." PLEASE get out your notebook and write down the following symbols and their meanings:

Use the following scenario for the questions below:

From a large group of people who signed a card saying they intended to quit vaping, 1000 people were selected at random. It turned out that 210 (21%) of these individuals had not vaped over the past 6 months. 

Since we do a lot of small group work in AP Statistics, we’ve decided to sample 2 students from a group of 4 and take the average of their scores to get an estimate for how well students in this group performed on the exam.  **Note: usually people wouldn’t use a sample and population this small, but we’re starting small to help you visualize what we’re doing.**

For this scenario, our population will be 4 students with the following scores: Alexis - 3, Bert - 4, Chris - 5, Devin - 5

Since we do a lot of small group work in AP Statistics, we’ve decided to sample 2 students from a group of 4 and take the average of their scores to get an estimate for how well students in this group performed on the exam. 

For this scenario, our population will be 4 students with the following scores: 3,4,5,5

Use the NetLogo model below to simulate choosing two students (n=2) at a time from this population (N=4).

1) Click "setup"  to start the model. If you are bothered by a person being cutoff on the edge of the screen, click "setup" again.

2) Click "collect sample" to choose your first sample, and record your results in the table below before pressing the button again.

3) Continue pressing "collect sample" and entering data into the table below until all possible samples have been chosen.

*Note: you may have to add additional rows to the data table. 

What you created on the previous page was the sampling distribution of AP scores for that group of 4 students. You took all six possible samples (n=2) from a population of four students (N=4). Sampling distributions are an important concept in Statistics and understanding what they are is the key to everything we do for the rest of the year.

A sampling distribution shows all possible samples of size n taken from a population of size N. In real-life scenarios, we don't create the entire sampling distribution by hand, or even using a computer, because our population is much larger (or it's size is unknown).  For illustrative purposes we will use a NetLogo model to simulate taking samples of AP Statistics exam scores from last year. There were 48 students in our classes last year, and we’ll take samples of 2 students at a time.

Here's the new scenario: 

We ran the model from the previous page until we collected every possible sample of 2 students. Below you can see the ENTIRE sampling distribution for our situation (n = 2, N = 48 students).