Question

Given the following data, determine the Chi-Square obtained statistic: a b c d 7 7 10 6 6 1 3 1

Answer 1

Chi-Square Test of independence
	Observed Frequencies
	0
0	a	b	c	d			Total
e	7	7	10	6			30
f	6	1	3	1			11
Total	13	8	13	7			41
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	a	b	c	d			Total
e	13*30/41=9.512	8*30/41=5.854	13*30/41=9.512	7*30/41=5.122			30
f	13*11/41=3.488	8*11/41=2.146	13*11/41=3.488	7*11/41=1.878			11
Total	13	8	13	7			41
	(fo-fe)^2/fe
e	0.6635	0.2245	0.025	0.151
f	1.8095	0.6123	0.068	0.411

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   3.9640