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Testing the Distribution of a Categorical Variable

Chapter 10 - Day 2 - Lesson 10.1

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?
Answer Key (coming soon!):

We’re introducing Chi-Square tests today, specifically the Chi-Square 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 Chi-Square are different from those we’ve done before because we don’t write equations and inequalities like we did in chapter 9.  For Chi-Square 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 Chi-Square test statistic.  There are two important parts to Chi-square, 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 Chi-Square 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.

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