Question

Q1) Is there a relationship between marital status and happiness? The data in the table show the marital status and happiness of individuals who participated in the General Social Survey. Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance. Round Evalues to two decimal places. (Chapter 12) Marital Status Not Row Happiness Married married Total Very happy 600 290 890 Pretty happy 720 955 1675 Not too happy 95 120 215 Column Total 1415 1365 2780 a. Write both alternative and null hypothesis. b. Find test statistics (show formula and final answer with two decimals) c. Find P-value (round to 3 decimal places)

Answer 1

a) H0: There is no relationship between martial status and Happiness
H1: There is relationship between martial status and Happiness

b) From the given data, the observed frequencies are

	Married	Not married	Total
Very Happy	600	290	890
Pretty Happy	720	955	1675
Not too happy	95	120	215
Total	1415	1365	2780

The Expected frequencies are

	Married	Not married	Total
Very Happy	453.00	437.00	890
Pretty Happy	852.56	822.44	1675
Not too happy	109.43	105.57	215
Total	1415	1365	2780

The Chi-square contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
600	453.00	47.699
290	437.00	49.4463
720	852.56	20.6119
955	822.44	21.3669
95	109.43	1.9036
120	105.57	1.9733
	Total:	143.001

Degrees of freedom: 2

Test Statistic, X^2: 143.00

c) P-Value: 0.000

Since P-value < alpha 0.05 so we reject H0

Thus we conclude that  there is relationship exist between martial status and Happiness. i.e. martial status and Happiness are dependent