Question

1. Use this data from the 2006 GSS to determine if there is a significant relationship between marital status and happiness. Use the five step model and describe each step.

	MARITAL STATUS
	MARRIED	DIVORCED	WIDOWED	SEPARATED	NEVER MARRIED	TOTAL
VERY HAPPY	600	93	63	19	144	919
PRETTY HAPPY	720	304	142	51	459	1676
NOT TOO HAPPY	93	88	51	31	127	390
TOTAL	1412	485	256	101	730	2984

Answer 1

Let us assume the significance level to be 5%.

Chi-Square Independence test - Results

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables - Marital Status and Happiness are independent Ha​: The two variables - Marital Status and Happiness are dependent This corresponds to a Chi-Square test of independence. (2) Degrees of Freedom The number of degrees of freedom is df = (3 - 1) * (5 - 1) = 8 (3) Critical value and Rejection Region Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df = (3 - 1) * (5 - 1) = 8, so the critical value is 15.5073. Then the rejection region for this test becomes R={χ2:χ2>15.5073}. (4)Test Statistics The Chi-Squared statistic is computed as follows: (5)P-value The corresponding p-value for the test is p=Pr(χ2​>236.4048)=0 (6)The decision about the null hypothesis Since it is observed that χ2=236.4048>χ2_c​rit=15.5073, it is then concluded that the null hypothesis is rejected. (7)Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables - Marital Status and Happiness are dependent, at the 0.05 significance level. Conditions: a. The sampling method is simple random sampling. b. The data in the cells should be counts/frequencies c. The levels (or categories) of the variables are mutually exclusive.

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!