Question

In the data below the rows define population groups A,B,C,D and the columns are education levels P,Q,R,S,T 25 106 58 14 203 75 38 179 231 90 538 17 24 10 56 34 67 38 144 341 404 24 19 171 991 50 The last row and column give row and column totals. The null hypothesis is that the data are not related. Find the value of

Answer 1

Null hypothesis is that the data are not related.

Here degree of freedom = (r - 1) * (c - 1) = (4 - 1) * (5 -1) = 12

$\chi^2$ = CHIINV(0.05, 12) = 21.0207

Expected table is given below.

	P	Q	R	S	T	Total
A	15.36	40.72	4.24	10.90	3.78	75
B	69.85	185.12	19.27	49.55	17.20	341
C	82.76	219.33	22.83	58.70	20.38	404
D	35.03	92.83	9.66	24.85	8.63	171
Total	203	538	56	144	50	991

Here is the chi-quare table

	P	Q	R	S	T	Total
A	6.04	0.18	0.14	3.19	0.84	10.40
B	18.71	0.20	0.27	4.88	8.66	32.71
C	7.41	0.62	0.06	1.17	0.64	9.90
D	12.62	0.09	0.01	6.96	12.47	32.15
Total	44.78	1.09	0.48	16.21	22.61	85.17

$\chi^2$ = 85.17