1. Section 4.1

3. Sampling from a population
Define the population we want to describe
Say exactly what we want to know/describe (about the population)
Decide how to choose a sample from the population

4. How to Sample BADLY
Let’s say that I want to know what time, on average, Elizabeth high school students wake up in the morning
So I get here really early, stand in front of the front door, and ask the first ten students: “what time did you wake up this morning?”
I then take the mean of these ten students, which is 5:43 AM, and I conclude that EHS students, on average, wake up at 5:43 each morning
Any problems with this?

5. How to Sample BADLY YES, there are problems with this
The first ten students who get here are probably also students who wake up earlier. So I am NOT getting a good estimation of the average
Also (less importantly), if I only ask those who enter through the front door, I am missing the people who come to school on the bus.
So I decide that my 5:43 estimate is not a great one. I decide on a new plan

6. How to Sample BADLY
So my 5:43 estimate is bad, and I decide to take a new sample
When AP Stats starts at 9:40, I ask the entire class what time they woke up, and I calculate the mean.
I find that they, on average, woke up at 7:22. Do I have a better estimate for what time EHS students wake up now?

7. How to Sample BADLY Maybe, maybe not
It is possible that more Stats students have 1st/5th hour off, so they get to sleep in more, and don’t have to wake up as early, on average
Or maybe AP students have more work than other students, so they wake up earlier in the morning to complete it
Either way, Stats students may not be a very good representation of the entire school

8. How to Sample BADLY
These methods that I chose are called convenience samples
I just take people who are convenient (the first 10 people in the building, or, even more convenient, the Stats students who have to come to my room anyway)
DON’T DO THIS

9. How to Sample BADLY Convenience samples introduce bias
Bias: If one or more outcomes is systematically favored over others
Book’s definition
When I just took the first ten people into the building, I was clearly OVER-estimating how early students wake up
So I was systematically favoring that outcome
Basically, any time your sample is not representative of the population, you are likely to get bias

10. Another Way to Sample Badly
So, frustrated, I decide to choose another sampling method
Instead of choosing people, I decide to let them choose me!
I send an out to the entire school asking what time they usually wake up in the morning
I get 82 responses, and find that the average time for students to wake up is 6:51 AM.
Finally! I have an actual average…right?
The AP Stats class tells me that this is incorrect. Why?

12. How to Sample Well
So what should I do instead?

13. How to Sample Well So what should I do instead? SIMPLE RANDOM SAMPLE!
“SRS” for short
Eliminates bias
No more favoritism by the researcher
No more self-selection by subjects
Literally just randomly select individuals from the population
So that every individual has an equal chance to be chosen

14. How do we make sure that it is random?
3 options:
Use random.org
Not really an option during your AP Test
Use Table D in your book
Table D is just tons of random digits
Example on next slide
Use your calculator
We’ll do this later also

17. Using Random Digits (Table D)
This is a good way to generate a random sample
You’ll get a different random sample depending on what line you use
This is okay—it’s RANDOM
So there may be some questions (on HW, tests, etc.) where you get a different sample from other people in the class
Again, that’s okay—just be sure to carefully describe how you’re getting that sample
How you’re numbering the individuals, what line you’re starting with, etc.

18. Using your Calculator MATH-----PROB-----randInt
randInt(lower, upper, number to sample)
We had 28 hotels to choose from, so we’ll use the following syntax:
randInt(1, 28, 4)
(I’m choosing 4 numbers between 1 and 28)
And most of us will get the following 4 numbers:
27, 26, 5, 15
Wait a minute…if it’s random, how can we all get the SAME “random” numbers?

19. Pseudo-Randomness
For the purposes of this class, and the AP test, we can think of Table D and the randInt function as being random
And it is random in the sense that each number has an equal chance of being chosen
But it is predictable—it follows a pattern
Because it is predictable, it is called pseudo-randomness
Not a big deal for our purposes
If you want a TRULY random number/list, use

20. Homework Time
Next class we will discuss alternatives to the simple random sample