Question

Recorded here is the frequency distribution of the blood types of 120 persons ?

Blood Type : O A B AB Total

Frequency : 44 35 25 16 120

Test the hyphotesis that the probability of the blood types O,A,B and AB is the ratios 3:4:1:2.

a) State the null hyphotesis and the alternative hyphotesis

b) Find the test statistic

c) If the significiancy level is 5%, find the critical value(s) and shade the rejection region(s)

d) Base one the type -I error alpha and the rejection region(s) , given above, what is the conlusion?

Answer 1

a)

The sample size is 120 person and the research want to test whether the proprtion of blood groups of O, A, B and AB are in the ratios 3:4:1:2. Hence the expected value of blood groups are,

b)

The Chi square test is used to test the hypothesis,

Blood Type	Observed frequency, Oi	Expected frequency, Ei
O	44	36
A	35	48
B	25	12
AB	16	24

The chi square statistic is obtained using the formula,

The critical value of chi square for two tailed test can be obtained using the chi square distribution table for significance level = 0.05 and degree of freedom = 4-1=3

d)

For 5% significance level, the critical value is,

The null hypothesis is rejected. Hence there is a sufficient evidence that some of the proportions differ from the claimed proportions