"Suppose you’re on a game show, and you’re given a choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say number 1, and the host, who knows what’s behind the doors, opens another door, say number. 3, which has a goat. (He will always show you a goat.) He says to you, ‘Do you want to pick door number 2?’ Is it to your advantage to switch your choice of doors?”
Simulations of the three doors problems
Click on the door and choose to stay or switch (from UCSD)
Another click on the door and choose to stay or switch (from Math Warehouse)
Simulate multiple random outcomes of three doors problem at once (Good for filling out "Winning door" column of the handout)
Other sites you can use for generating "winning doors"
Random.org's list randomizer (put "goat" on the first line, "goat" on the second line, and "car" on the third line, and then click "randomize")
Vassarstats randomizer (scroll down, put "3" in the space for "n", click "randomize," then put the car in whatever line "1" appears)
Entering data
Analyzing data
2 X 2 chi-square tests
Before doing these chi-square tests, copy down the following chart on a piece of paper.
Stayed Switched
Lost ___ ___
Won ____ ____
Then, you will need to put numbers in the four blanks. The data you need are here.
Suppose that,
in the stay condition, you had 100 wins and 200 losses, and that
in the switch condition, you had 240 wins and 120 losses.
In that case, your paper would look like this:
Stayed Switched
Lost 200 120
Won 100 240
In that case, you could calculate a chi-square by entering the following numbers into VassarStats.
Select the number of rows:
Select the number of columns:
2
2
Data EntryQ
Regardless of which site you use, record the value of the chi square and the p value.
You can try analyzing your own data alone as well as the entire class's data. You may find that your own data, by themselves, are not statistically significant. However, you will probably find that the class's data are statistically significant.