Practice Chi-Square Test in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A family of hypothesis tests that use the chi-square statistic to compare observed frequencies to expected frequencies. The three main types are: goodness-of-fit (does data match a claimed distribution?), test of independence (are two categorical variables related?), and test of homogeneity (do different populations have the same distribution?).

You expect a die to land on each face about \frac{1}{6} of the time. You roll it 600 times and compare what you observed to what you expected. If the differences are small, the die is probably fair. If they're large, something is off. The chi-square statistic measures 'how far off are the observed counts from what we expected?'

Example 1

medium
A die is rolled 60 times. Observed: 1→8, 2→12, 3→9, 4→11, 5→13, 6→7. Conduct a chi-square goodness-of-fit test at \alpha=0.05.

Example 2

hard
A 2×2 table: Men: 30 prefer A, 20 prefer B. Women: 15 prefer A, 35 prefer B. Test independence of gender and preference at \alpha=0.05.

Example 3

easy
For a chi-square test with observed=15, expected=20 for one category, calculate that category's contribution to the \chi^2 statistic.

Example 4

hard
A survey of movie preferences across three age groups produces a 3×4 contingency table (3 age groups, 4 movie genres). State H_0 and H_a, calculate degrees of freedom, and explain what a significant result would mean.
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