Suppose, in Example 13.1, that a random sample of 200 stomach cancer patients yielded 92 having blood type A, 20 having blood type B, 4 having blood type AB, and 84 having blood type O. Are these data significant enough, at the 5 percent level of significance, to enable us to reject the null hypothesis that the blood type distribution of stomach cancer sufferers is the same as that of the general population?
Example 13.1
It is known that 41 percent of the U.S. population has type A blood, 9 percent has type B, 4 percent has type AB, and 46 percent has type O. Suppose that we suspect that the blood type distribution of people suffering from stomach cancer is different from that of the overall population. To verify that the blood type distribution is different for those suffering from stomach cancer, we could test the null hypothesis
H0:
P
1
= 0.41,
P
2
= 0.09,
P
3
= 0.04,
P
4
= 0.46
where P1
is the proportion of all those with stomach cancer who have type A blood, P2
is the proportion of those who have type B blood, P3
is the proportion who have type AB blood, and P4
is the proportion who have type O blood. A rejection of H0
would then enable us to conclude that the blood type distribution is indeed different for those suffering from stomach cancer. In the preceding scenario, each member of the population of individuals who are suffering from stomach cancer is given one of four possible values according to his or her blood type. We are interested in testing the hypothesis that P1
= 0.41, P2
= 0.09, P3
= 0.04, P4
= 0.46 represent the proportions of this population having each of the different values.