Question

A sample of 150 was obtained of men with each of three types of cancer, and the following data show blood types for each. Use an appropriate test, determine if blood type of cancer type are related. (Contingency table )

		Blood Type
Cancer Type	O	A	B	AB
Colon	61	65	18	6
Lung	69	57	15	9
Prostate	73	60	12	5

Answer 1

Claim: blood type of cancer type are related.

The null and alternative hypothesis is

H0: blood type of cancer type are not related.

H1: blood type of cancer type are related.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

		Blood Type
Cancer Type	O	A	B	AB	Total
Colon	61	65	18	6	150
Lung	69	57	15	9	150
Prostate	73	60	12	5	150
Total	203	182	45	20	450

O	E	(O-E)	(O-E)^2	(O-E)^2/E
61	67.66667	-6.66667	44.44444	0.656814
65	60.66667	4.333333	18.77778	0.309524
18	15	3	9	0.6
6	6.666667	-0.66667	0.444444	0.066667
69	67.66667	1.333333	1.777778	0.026273
57	60.66667	-3.66667	13.44444	0.221612
15	15	0	0	0
9	6.666667	2.333333	5.444444	0.816667
73	67.66667	5.333333	28.44444	0.420361
60	60.66667	-0.66667	0.444444	0.007326
12	15	-3	9	0.6
5	6.666667	-1.66667	2.777778	0.416667
			Total	4.14

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 3 - 1) * (4 - 1) = 2 * 3 = 6
Critical value = 12.592

( From chi-square table)

Test statistic < critical value we fail to reject the null hypothesis.

Conclusion:

Blood type of cancer type are not related.