Question

A relationship expert is interested in the relationship between divorce and general happiness. A sample of 1,212 individuals who reported their marital status as either "married" or "divorced" was selected and individuals in the two groups were asked to rate their general level of happiness (either "Not Too happy" or "Pretty/Very Happy"). The table below summarizes the data.

Group	Not Too Happy	Pretty/Very Happy	Total
Divorced (Group 1)	60	255	315
Married (Group 2)	64	833	897

Calculate the test statistic of the test of the hypothesis that the proportion of divorced people who are "Pretty/Very Happy" is smaller than the proportion of married people who are "Pretty/Very Happy". Take all calculations toward the answer to four (4) decimal places, and report your answer to two (2) decimal places.

Answer 1

From the given data,

Let p₁, p₂ denote the proportion of individuals who are "Pretty/Very Happy" among those who are married or divorced respectively.

We are asked to test:

Vs

The appropriate statistical test to test the above hypothesis would be a Z test for 2 proportions.

From the given sample, by definition of proportion, the samples proportions are computed as follows:

The test statistic is given by:

where,

Substituting the values,

= -6.01

Test statistic = -6.01