A random sample of 150 recent donations at a certain blood bank reveals that 82 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of population having type A blood? Carry out a test of appropriate hypotheses using a significance level of 0.01. Would your conclusion have been different if a significance level of 0.05 has been used?

We reject H₀ Porcentage of type A blood donations differs from 40% (porcentage of population having type A blood)

Step-by-step explanation:

We are going to develop a proportion test.

Information we have:

Proportion P₀ = 40 % P₀ = 0,4 (porcentage of population having type A blood)

Sample size n = 150

Sample mean P = 82 / 150 P = 0,5466

As P₀ = 0,4 Q₀ = 0,6 P₀*Q₀ = 0,24

1.-Test Hypothesis:

H₀ null hypothesis P₀ = 0.4

Hₐ alternative hypothesis P₀ ≠ 0.4

2. - signficance level

a) α = 0.01 we have a two tail-test α/2 = 0.005

b) α = 0.05 α/2 = 0.025

Then from t-student table we get t (c) n = 150 df = 149

a) α/2 = 0.005 t (c) = 2.581

b) α/2 = 0.025 t (c) = 1.962

3.-Compute t (s)

t (s) = (P - P₀) / √P₀Q₀/n

Plugging in known values

t (s) = [ (0.5466 - 0,4) * √150 ] / √0.24

t (s) = 0,1466 * 12.25 / 0.4899

t (s) = 3.6657

Compare t (s) and t (c)

t (s) > t (c) 3.6657 > 2.581

Then t (s) is out of the acceptance region we reject H₀.

Simple inspection led us see that for

α/2 = 0.025 t (c) = 1.962

The situation is the same