Testing the Distribution of a Categorical Variable
Chapter 10  Day 2  Lesson 10.1
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Learning Targets

State hypotheses for a test about the distribution of a categorical variable.

Calculate expected counts for a test about the distribution of a categorical variable.

Calculate the test statistic for a test about the distribution of a categorical variable.
Activity: Which color M&M is the most common?
We’re introducing ChiSquare tests today, specifically the ChiSquare test for Association. For today’s lesson you will need plenty of M&M candies. We bought big bags and some Dixie cups for passing them out. This was helpful because we could portion everything out beforehand which helped save time in class. According to the manufacturer, the color distribution of candies should be 13% Brown, 14% Yellow, 20% Orange, 16% Green, 24% Blue, and 13% Red. Students should count up the number of each color that they have and report their data on the board. Find the class totals for each color.
The hypotheses for ChiSquare are different from those we’ve done before because we don’t write equations and inequalities like we did in chapter 9. For ChiSquare tests for goodness of fit the hypotheses are:
Null Hypothesis: The claimed distribution is correct.
Alternative Hypothesis: The claimed distribution is incorrect.
You will want to discuss this with the class before moving on. After going through the hypotheses, students will work on calculating the ChiSquare test statistic. There are two important parts to Chisquare, observed values and expected values. The observed values are given in the problem and the expected values are calculated using the claimed percent × sample size.
We created scaffolding with a table so that the students can work through calculating the ChiSquare test statistic by hand using the formula Χ²=(Observed – Expected)² / Expected. After students work through the activity you can also talk about how use a spreadsheet to do the calculations for you. Here is an Excel spreadsheet that we used.