Question

Culture\Custom	X	Y	Z	Total
A	49	71	88	208
B	102	24	24	150
C	9	39	43	91
Total	160	134	155	449

Does this data provide enough evidence at the α = 0.05 confidence level that there is dependence based on someone’s culture and a particular custom they uphold? (X,Y,Z are customs and A,B,C are cultures)

Answer 1

Hypotheses are:

H0: There is no dependence based on someone’s culture and a particular custom they uphold.

Ha: There is dependence based on someone’s culture and a particular custom they uphold.

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

Culture\Custom	X	Y	Z	Total
A	74.12	62.076	71.804	208
B	53.452	44.766	51.782	150
C	32.428	27.158	31.414	91
Total	160	134	155	449

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
49	74.12	8.513416082
102	53.452	44.09392172
9	32.428	16.92584137
71	62.076	1.282907662
24	44.766	9.632907921
39	27.158	5.163596878
88	71.804	3.653144894
24	51.782	14.90555645
43	31.414	4.273107404
Total		108.4444004

Following is the test statistics:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (3-1)*(3-1) = 4

The p-value is: 0.0000

Conclusion: Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that there is dependence based on someone’s culture and a particular custom they uphold.

Excel function used for p-value: "=CHIDIST(108.44, 4)"