Chapter 11
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12

All Chapters

Experience First

In this lesson, we revisit the Taco Tongue, Evil Eyebrow context from Chapter 5. Back in Chapter 5, students determined if the two special skills were independent (no association) for a sample. In this lesson (and Lesson 11.4), students will be trying to determine if there is an association for a population, based on sample data. 

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We suggest letting students work in small groups on questions #1-3, then doing a whole group discussion for #4-5, and then handing it back to students for #6. 

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Formalize Later

Once question #3 is completed, we can say with certainty that the two special skills are associated for the sample of 600 high school students. We want to determine if our data provides convincing evidence of an association for the population of all high school students. We obviously have some evidence that this is true for the population, because the proportions are different for the sample, but maybe this happened purely by chance due to sampling variability. This is why we need a significance test.

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To help explain the formula for the expected counts, we need to remember that these values are calculated assuming the null hypothesis is true. This means that taco tongue and evil eyebrow are not associated. Start by noting that for the whole sample of students, 480/600 = 80% are yes taco tongue. So 80% of the yes evil eyebrow students should be yes taco tongue and 80% of the no evil eyebrow students should be yes taco tongue. 

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200 X 80% = 160, which is really 200 X (480/600)

400 X 80% = 320, which is really 400 X (480/600)

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As foreshadowing for a follow-up analysis in tomorrow's lesson, you might want to point out that the yes evil eyebrow, no taco tongue created the largest contributor to the chi-square test statistic, because the observed count (20) was much less than expected (40).