[AP Statistics] 12.2a Chi-Square test for Homogeneity

One thing I've been curious about: does the AP Statistics class period you are in affect which test you did best at this semester? My lessons always end up playing out slightly differently, and students in each class ask different questions.

There are 4 graded tests so far this semester (Chapters 7, 8, 9, and 10). For each person in each class period, I looked in my grade book and noted the test they did best on out of the 4. Turns out no one did best on Chapter 9 so we will ignore it for convenience!

Observed Counts for best test:

Just looking at the data, do you think the difference between the periods could be due to random chance?

What are the sample(s) and variable(s) in this study?

In general terms, what should be the null hypothesis for our significance test?

In general terms, what should be the alternative hypothesis for our significance test?

Like our other Chi-Square test, we will need to calculate the expect count

Observed:

What is the expected count for Students in Period E doing best on Chapter 7?

Round to 1 decimal place

What is the expected count for Students in period G doing best on Chapter 10?

Round to 1 decimal place

I'm only going to make you calculate two of those since it is tedious. Your calculator will take care of the rest soon.

Now we need to check our conditions, which are the same as for the other Chi-Square test

Do we meet the Large Counts condition?

Explain

The degrees of freedom are calculated in a different way than last time. What are the degrees of freedom for this study?

The Chi-Square test statistic is calculated the same way as we did last time. We will let our calculator do the heavy lifting.

Because our data is in a 2 way table, we need to enter it into a matrix instead of a list.

Enter the OBSERVED data into matrix A: 2nd->Matrix->Edit->[A]

Stat->Test-X^2-Test shows the following, indicating that it will read the observed in Matrix [A] and output the expected values into Matrix [B]

When you hit enter, you should see the X^2 test statistic. Type it below.

Round to 1 place

You should also see the p-value. Type it below

Round to 2 places

If you hit 2nd->Matrix->[B] and hit enter, you can see the expected values that your calculator calculated.

Note: It might actually be easier to see the values if you go 2nd->Matrix->Edit->[B]

What is the expected value for Period G students who did best on Chapter 7 (2nd row first column)?

Round to 1 place

Do we have convincing evidence that 2 classes differ in terms of which test they did best?

a=0.05

Explain

What should be the expected value for the Red/Red cell?

Round to 1 place

How many degrees of freedom?

What is the chi-square test statistic?

Round to 2 places

What is the p-value?

Round to three places

What is your conclusion at the a=0.05 level?

STATE

PLAN (You probably want to complete the Do step first to get the table of expected values)

For my class, you don't need to recreate the table for the plan step like they do in the sample. If this comes up on the AP exam, you SHOULD recreate the table

DO

Record P-Value, Degrees of Freedom, and the Chi Square Test Statistic

CONCLUDE

Are there any problems above that you would like to go over in class? Indicate the question numbers below (Numbers refer to the Formative question number). I'll try to cover anything that is highly requested.