• Complete a chi-square test of independence
• Write the conclusion of a chi-square test of independence in context of the problem

In the test of independence, we consider one population and two categorical variables.

The mechanics of performing a chi-square test of independence are the same as those for the chi-square test of homogeneity.

The first step of any hypothesis test is to write its hypotheses.

the null and alternative hypotheses

The null and alternative hypotheses for chi-square test of independence are the following:

• [latex]H_0[/latex]: The two variables of interest are independent.
• [latex]H_A[/latex]: The two variables of interest are not independent.

As usual, the null hypothesis is a statement of no change in that if the two variables are independent in the population, knowing the value of one variable does not change the likelihood that the second variable will have a particular value.

Sometimes the null and alternative hypotheses are written with slightly different wording, but they are equivalent to the previous wording:

• [latex]H_0[/latex]: The two variables of interest are not associated.
• [latex]H_A[/latex]: The two variables of interest are associated.

The second step in a hypothesis test is to check the conditions for the hypothesis test.

conditions for [latex]\chi^2[/latex] test of independence

1. The data represent the counts for two categorical variables measured for individuals in one sample from one population.
2. Independence/Randomness Condition: The sample from our population should be independent, random sample or independent sample that can be considered representative of the population.
3. Large Sample Size Condition: The sample size must be large enough so that the expected count in each cell is at least five.