Question

State the null and alternative hypotheses for a chi-square homogeneity test
a. without using the terms homogeneous and nonhomogeneous.
b. using the terms homogeneous and nonhomogeneous

Short answer

Part (a)

Without using the terms homogeneous and nonhomogeneous,

Null hypothesis,
H₀ : The distributions of the variable are the same for all the populations.
Alternative hypothesis,
H_a : The distributions of the variable are not all the same (i.e., the distributions differ for at least two of the populations).

Part (b)

Using the terms homogeneous and nonhomogeneous

Null hypothesis,
H₀ : The populations are homogeneous with respect to the variable.
Alternative hypothesis,
H_a : The populations are nonhomogeneous with respect to the variable.

Step-by-step solution

Part (a) Step 1. Given information

Given test is a chi-square homogeneity test

Part (a) Step 2. without using the terms homogeneous and nonhomogeneous.

Without using the terms homogeneous and nonhomogeneous, the null and alternative hypotheses for a chi-square homogeneity test:
Null hypothesis,
H₀: The distributions of the variable are the same for all the populations.
Alternative hypothesis,
H_a : The distributions of the variable are not all the same (i.e., the distributions differ for at least two of the populations).

Part (b) Step 1. Given information

Given test is a chi-square homogeneity test

Part (b) Step 2. using the terms homogeneous and nonhomogeneous 

Using the terms homogeneous and nonhomogeneous, the null and alternative hypotheses for a chi-square homogeneity test:
Null hypothesis,
H₀ : The populations are homogeneous with respect to the variable.
Alternative hypothesis,
H_a : The populations are nonhomogeneous with respect to the variable.