Question

1. In the 2008 General Social Survey, incomes of married respondents were classified as above average, average, and below average. Respondents also answered a question about marital happiness as not happy, pretty happy, or very happy. The results are below:

	Marital Happiness
Income	Not Happy	Pretty Happy	Very Happy	Totals
Above Average	123	105	7	235
Average	291	151	17	459
Below Average	172	83	6	261
Totals	586	339	30	955

Conduct an appropriate test to determine whether or not there is a statistically significant association between marital happiness and income at the 5% significance level.

a) Which is the independent variable and which is the dependent variable?

b) For individuals with average income, what percentage of individuals report their marital happiness as “pretty happy?”

c) Are the basic assumptions of the hypothesis test satisfied?

d) What are the null and alternative hypotheses?

e) Based on the significance level at which you are testing, what is (are) the critical value(s) for the test?

f) Calculate the appropriate test statistic, showing all your work. You should explicitly display (1) expected values for each cell and (2) the test statistic contribution of each cell in addition to calculating the overall test statistic.

g) Calculate the corresponding p-value from the appropriate table or online calculator.

h) What conclusions can you draw from the hypothesis test? Be sure to comment on evidence from both the test statistic and p-value.

Answer 1

a) Which is the independent variable and which is the dependent variable?

Independent variable is Income

Dependent variable is marital happiness

b) For individuals with average income, what percentage of individuals report their marital happiness as “pretty happy?”

c) Are the basic assumptions of the hypothesis test satisfied?

Yes The frequencies of all the cells are > 5

d) What are the null and alternative hypotheses?

Null hypothesis: Income is independent of Marital status

Alternate hypothesis : Income is dependent on marital status

e) Based on the significance level at which you are testing, what is (are) the critical value(s) for the test?

Level of significance = 5%

Critical value = 9.488

f.

		Marital happiness
Income	Not happy	Pretty happy	Very happy
Above average	123	105	7	235
Average	291	151	17	459
Below average	172	83	6	261
Totals	586	339	30	955
Expected frequencies
	144.199	83.41885	7.382199
	281.6482	162.933	14.41885
	160.1529	92.64817	8.198953
				955
(Oi-Ei)^2/Ei
	3.116497	5.583224	0.019788
	0.310518	0.873955	0.462058
	0.876377	1.004738	0.589757
		Test statistic	=	12.83691

g Calculate the corresponding p-value from the appropriate table or online calculator.

Pvalue = 0.012

h What conclusions can you draw from the hypothesis test? Be sure to comment on evidence from both the test statistic and p-value.

Test statistic is > critical value and pvalue < 0.05

Hence Ho is rejected

WE can conclude that marital status is dependent on income

Excel calculations are as follows