Question

It is believed that the proportions of people with A, B, O and AB blood types
in the population are 0.4, 0.2, 0.3 and 0.1. When 400 randomly picked people
were examined, the observed numbers of each type were 148, 96, 106 and
50. At the 5% level of significance, test the null hypothesis that these data
bear out the stated belief

Answer 1

n=4

α=0.05

df=n-1=3

$H_0: P_1=0.4, P_2=0.2, P_3=0.3, P_4=0.1$

$H_1:$ Proportion differs from the given proportion.

Test-statistic:

$χ^2 = \sum^n_i \frac{(O_i-E_i)^2}{E_i} \\ χ^2 =8.23$

Critical value:

α=0.05

df=3

$χ^2_{0.05,3}=7.815$ (Chi-square table)

Since $χ^2 =8.23 > χ^2_{0.05,3}=7.815$ we reject H₀ at the 5% level of significance.

There is insufficient evidence to conclude that proportions of people with A, B, O and AB blood types in the population are 0.4, 0.2, 0.3 and 0.1.