** please show work** A social scientist is interested in the relationship betwe
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** please show work**
A social scientist 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 Happy/Very Happy"). The table below summarizes the data.
Calculate the test statistic of the test of the hypothesis that the proportion of divorced people who are "Pretty Happy/Very Happy" is smaller than the proportion of married people who are "Pretty Happy/Very Happy". Take all calculations toward the answer to four (4) decimal places, and report your answer to two decimal places.
Not Too Happy Pretty Happy/Very Happy Total Divorced (Group 1) 60 255 315 Married (Group 2) 64 833 897Explanation / Answer
This is the case of proportion and the sample sizes are large to satisfy the normality assumptions. Here z-test of proportions will be the test statistics
z = (p1^ -p2^)/SE (p1-p2)
p1^ = 255 / 315 = 0.8095
p2^ = 833 / 897 = 0.9287
SE (p1-p2) = Ö [P *Q * ((1/n1) + (1/n2))]
P =(x1+x2)/(n1+n2)
= (255+315)/(315+897)
= 0.8977
Q = 1 – P = 1 – 0.8977 = 0.1023
n1 = 315
n2 = 897
SE (p1-p2) = Ö [P *Q * ((1/n1) + (1/n2))]
= Ö [0.8977 *0.1023 * ((1/315)+(1/897))]
= 0.0198
z = (p1^ -p2^)/SE (p1-p2) = (0.8095 0 0.9287)/0.0198 = -6.01
Answer: z = -6.01
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