Question

Below are hypothetical data on the relationship between sex and marital satisfaction. Conduct a chi-square test to example the association between these two variables. Be sure to show all steps, including writing your hypotheses, calculating expected frequencies for each cell, calculating the chi-square statistic, deciding whether to reject the null, and explaining what this decision means.

	Sex
Marital Satisfaction	Male	Female		Row Total
Satisfied	309	255		564
Unsatisfied	107	278		385
Column Total	416	533		949

Answer 1

We first compute the expected frequencies for each of the 4 cells here as:

E(male, satisfied) = n(male)n(satisfied) / n(total)
E(male, satisfied) = 416*564 / 949 = 247.23

Similarly other 3 expected values are computed here to get:

E(male, unsatisfied) = 168.77,
E(female, satisfied) = 316.77,
E(female, unsatisfied) = 216.23

Using these values, the chi square test statistic value here is computed as:

Therefore 67.7256 is the required chi square test statistic value here.

The degrees of freedom here is computed as:
DF = (num of rows - 1)(num of columns - 1) = 1

Therefore the p-value here is computed as:

As the p-value here is approximately equal to 0, the test is significant and we can reject the null hypothesis here and conclude that we have sufficient evidence that the 2 variables are not independent and are associated.