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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

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Answer:

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

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

User Catalina Astengo
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