Question

A sample of 200 individuals are tested for their blood type is given in the first table, and the results are used to test the hypothesized distribution of blood types. The observed results are given in the second table. At the .05 level of significance, is there sufficient evidence to show that the stated distribution is incorrect?

Blood Type	A	B	O	AB
Percent	0.4	0.1	0.41	0.09

Blood Type	A	B	O	AB
Number	66	14	87	33

(a) Find the test statistic. (Give your answer correct to two decimal places.)

Answer 1

The null and alternative hypothesis is

H0: The population fits the given distribution.

H1: The population has a different distribution.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.

E = n*pi

n = 200

O	p	E	(O-E)	(O-E)^2	(O-E)^2/E
66	0.4	80	-14	196	2.45
14	0.1	20	-6	36	1.8
87	0.41	82	5	25	0.304878
33	0.09	18	15	225	12.5
				Total	17.05

Degrees of freedom = Number of E - 1 = 4 - 1 = 3

Critical value = 7.815

Test statistic > Critical value we reject null hypothesis.

Conclusion:

The population has a different distribution.