**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

<u>4 4 6.8 -2.8 7.84 1.96 </u>

<u>∑ 170 188.7 χ²= 12.43 </u>

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The critical region is <u>χ</u>²≥ χ²(0.05,3) = 7.82 for alpha = 0.05 and

<u>χ</u>²≥ 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.