Question

A random sample of 146 recent donations at a certain blood bank reveals that 81 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood

Answer 1

Answer:

We reject H₀  the actual percentage of type A donations differs from 40%

Step-by-step explanation:

Sample information:

sample size   n = 146

Type A   x₁  =  81   and   p₁  = 81 / 146     p₁  =  0,5547

then  q₁   =  1 - p₁    q₁  =  1  -  0,5547    q₁  =  0,4453

We choose as significance level  α  = 5%  α = 0,05   α /2  = 0,025

from z-table we find   z (c) = 1,96

National % of the population  ( μ  = 40 %  μ = 0,4 )

Test hypothesis

Null hypothesis                           H₀           p₁  =  μ

Alternative Hypothesis              Hₐ           p₁   ≠ μ

The Alternative hypothesis indicates that the test is a two-tail test

z(s) =  ( p₁  -   μ )/ √ p₁*q₁ / n

z(s) =  ( 0,5547  -  0,40 )/ √ 0,5547*0,4453 / 146

z(s) =  0,1547 / 0,041

z(s) = 3,77

Comparing  z(s)  and z(c)

z(s) > z(c)  

z(s) is in the rejection region. We reject H₀. Sample does not give evidence to support that the actual percentage of type A donations is equal to the national population