Chi-Square Test Math Example 4

Follow the full solution, then compare it with the other examples linked below.

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 H0H_0 and HaH_a, calculate degrees of freedom, and explain what a significant result would mean.

Solution

  1. 1
    H0H_0: age group and movie genre preference are independent
  2. 2
    HaH_a: age group and movie genre preference are associated (not independent)
  3. 3
    Degrees of freedom: (rows−1)(cols−1)=(3−1)(4−1)=2×3=6(\text{rows}-1)(\text{cols}-1) = (3-1)(4-1) = 2 \times 3 = 6
  4. 4
    Significant result: reject H0H_0; conclude that movie genre preference varies by age group — the distribution of genre preferences is different for different ages

Answer

H0H_0: independence. df=6. Significant result → age and genre preference are associated.
The chi-square test of independence asks whether two categorical variables are related. Degrees of freedom = (r-1)(c-1). A significant result means the variables are not independent — knowing someone's age provides information about their genre preference.

About Chi-Square Test

A hypothesis test that compares observed frequencies to expected frequencies using the chi-square statistic to assess independence or goodness of fit.

Learn more about Chi-Square Test →

More Chi-Square Test Examples

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-o

Example 2 hard

A 2×2 table: Men: 30 prefer A, 20 prefer B. Women: 15 prefer A, 35 prefer B. Test independence of ge

Example 3 easy

For a chi-square test with observed=15, expected=20 for one category, calculate that category's cont

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