Chi-Square Tests for Goodness of Fit (Lesson 11.2)
Chapter 11 - Day 2
Learning Targets
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Check conditions for a test about the distribution of a categorical variable.
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Calculate the P-value for a test about the distribution of a categorical variable.
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Use the four-step process to perform a chi-square test for goodness of fit.
Experience First
For this lesson, we will using the sample data collected in the previous lesson to evaluate the claim made by the company about the distribution of color. Students will use the 4-step process to perform a chi-square goodness of fit test.
Most of the hard work for this significance test was done in the previous lesson. In this lesson we add in the conditions for inference, the P-value, and the conclusion.
Students will use the Chi-square goodness of fit applet (part of the Traditional Inference applets at www.statsmedic.com/applets to find the P-value.
Warning: In the applet, students need to enter in the expected counts. Sometimes due to rounding, the sum of the expected counts does not equal the sample size. If this happens, adjust one of the expected counts slightly so that the sum of the expected counts equals the sample size.
Formalize Later
This is the first time students are seeing the picture of the chi-square distribution. Using the formula for the chi-square test statistic, explain why the distribution starts at 0 and is skewed to the right.
If the results are statistically significant, you may want to have students do a follow-up analysis. Here, we look at the contributions table at the bottom of the applet. These are the components that add up to give the chi-square test statistic. Find the largest component and explain it in the context of the problem.
"The largest component of the chi-square test statistic is for blue, because the observed count (74) was much less than the expected count (110.6)."
