Answer:
The proportions differ significantly from those in the general population.
Step-by-step explanation:
We state our null and alternative hypotheses as
H0: p1= 49/100, p2= 38/100, p3= 9/100 and p4= 4/100 for a multinomial distribution involving four categories and n= 170
against
Ha: pi≠ pi0 for at least one value of i= 1,2,3,4
The significance level is set at ∝= 0.05
The test statistic under H0 is
χ² = ∑ (Oi- ei)²/ei
which has approximate chi square distribution with 3d.f (n-1)
Computations: Under H0 the expected frequencies are
np10= Blood type O = 170 * 49/100= 83.3
np20 = Blood type A = 170 * 38/100= 64.6
np30 = Blood type B = 170 * 20/100= 11.76
np40 = Blood type AB = 170 * 4/100= 2.35
The value of χ² is computed as follows
Cell Observed Estimated (Oi-ei) (Oi-ei)² (Oi-ei)²/ei
Frequency Frequency
Oi ei
1 87 83.3 3.7 13.69 0.157
2 59 64.6 -5.6 31.36 0.531
3 20 34 -14 196 9.8
4 4 6.8 -2.8 7.84 1.96
∑ 170 188.7 χ²= 12.43
The critical region is χ²≥ χ²(0.05,3) = 7.82 for alpha = 0.05 and
χ²≥ χ²(0.01,3) = 11.34 for alpha = 0.01
As the calculated value lies in the critical region for both value of alpha we reject our null hypothesis and accept our alternate hypothesis. The proportions differ significantly from those in the general population.
