8.6 Carrying Out a Chi-Square Test for Homogeneity or Independence

Complete Chi-Square Test for Independence

Continuing the party/tax example:

${\chi^2 = 85.71}$, ${df = 1}$, ${p = P(\chi^2_1 \geq 85.71) \approx 0.000}$ (essentially 0)

Full solution using PHANTOMS: P: Association between party affiliation and tax opinion in the population
H: ${H_0}$: No association; ${H_a}$: There is an association
A: Random ✓; 10% condition ✓; all ${E_{ij} \geq 5}$ ✓
N: Chi-square test for independence, ${df = 1}$
T: ${\chi^2 = 85.71}$
O: ${p \approx 0.000}$
M: ${p < 0.05}$ → Reject ${H_0}$
S: We have convincing evidence of an association between party affiliation and opinion on the tax increase. Democrats were much more likely to support the tax (120/150 = 80%) while Republicans were more likely to oppose it (110/150 = 73%).