Answer:
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
