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13 June, 04:17

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?

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  1. 13 June, 05:47
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    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
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