Question

1)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.

1)__________

2)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 upper bound of the 95% confidence interval for the difference between the proportion of divorced and the proportion of married persons who are "Pretty/Very Happy." Take all calculations toward the answer to four (4) decimal places, and report your answer to three decimal places.

2)________

Answer 1

#1.
H0: p1 = p2
Ha: p1 < p2

n1 = 315
n2 = 897
p1cap = 255/315 = 0.8095
p2cap = 833/897 = 0.9287

pcap = (255 + 833)/(315+897) = 0.8977

SE = sqrt(0.8977*(1-0.8977)((1/315+1/897))
SE = 0.0198

Test statistics, z = (0.8095 - 0.9287)/0.0198
z = -6.0019

p-value = 0.0000

Reject the null hypothesis
Significant evidence to conclude that proportion of "Pretty/very happy" of divorced individuals is less than "Pretty/very happy" of married individuals.

#2.
z = 1.64
upper bound = (0.8095 - 0.9287) + 1.64*0.0198
upper bound = -0.0867