Question

Based on this table, calculate the number of Pacific people who are married that we would expect in the sample if we assume there is no association between marital status and ethnicity. Show your working.

Table of Counts:

European Maori Other Pacific Row Total
Married 65 6 2 5 78
Never 61 16 4 6 87
Other 9 2 7 1 19
Previously 14 2 0 0 16

Answer 1

H0: There is no assocation between material status and ethnicity

H1: There is assocation between material status and ethnicity

Let the los be alpha = 5%

The observed frequencies are

Response	Maori	Other	Pacific	Row	Total
Married	65	6	2	5	78
Never	61	16	4	6	87
Other	9	2	7	1	19
Previously	14	2	0	0	16
Total	149	26	13	12	200

The expected frequencies are

Response	Maori	Other	Pacific	Row	Total
Married	58.11	10.14	5.07	4.68	78
Never	64.815	11.31	5.655	5.22	87
Other	14.155	2.47	1.235	1.14	19
Previously	11.92	2.08	1.04	0.96	16
Total	149	26	13	12	200

The chisquare contribution values are

		Contribution
Oi	Ei	(Oi-Ei)^2 /Ei
65	58.11	0.8169
61	64.815	0.2246
9	14.155	1.8774
14	11.92	0.363
6	10.14	1.6903
16	11.31	1.9448
2	2.47	0.0894
2	2.08	0.0031
2	5.07	1.859
4	5.655	0.4844
7	1.235	26.9111
0	1.04	1.04
5	4.68	0.0219
6	5.22	0.1166
1	1.14	0.0172
0	0.96	0.96
	Total:	38.4197

Degrees of freedom: 9

Test Statistic, X^2: 38.4195
Critical X^2: 16.91895
P-Value: 0.0000

Here chisquare value > chisquare critical value and P-value < alpha 0.05 so we reject H0

Thus we conclude that there is assocation between material status and ethnicity