A random sample of 150 recent donations at a certain blood bank reveals that 82 were typeA blood. Does this suggest that the actual percentage of type A donations differs from 40%,the percentage of the population having type A blood? Carry out a test of the appropriatehypotheses using a significance level of .01. Would your conclusion have been different if asignificance level of .05 had been used?

Respuesta :

Answer:

No conclusion have been not different if a significance level of 0.05 had been used also

The calculated Z-value = 3.596 > 1.96 at 5% level of significance

Null hypothesis is rejected

Alternative Hypothesis is Accepted

The actual percentage of type A donations is not differs from 40%,the percentage of the population having type A blood.

Step-by-step explanation:

Explanation:-

Step(i):-

A random sample of 150 recent donations at a certain blood bank reveals that 82 were type A blood

Given sample size 'n' = 150

Sample proportion [tex]p = \frac{x}{n} = \frac{82}{150} =0.546[/tex]

Given Population proportion P = 40% =0.40

level of significance ∝ = 0.01

Step(ii):-  

Null Hypothesis:- H₀: p=0.40

Alternative Hypothesis:-H₁:p≠0.40

The test statistic

[tex]Z =\frac{ p^{-} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

a) 99% of level of Z-value

                  [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01}{2} } = Z_{0.005} = 2.576[/tex]

[tex]Z =\frac{ 0.546 - 0.40}{\sqrt{\frac{0.546(1-0.546)}{150} } }[/tex]

Z = 3.596

The calculated Z-value = 3.596 > 2.576 at 1% level of significance

Null hypothesis is rejected

Alternative Hypothesis is Accepted

The actual percentage of type A donations is not differs from 40%,the percentage of the population having type A blood.

b) 95% of level of Z-value

                  [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]

[tex]Z =\frac{ 0.546 - 0.40}{\sqrt{\frac{0.546(1-0.546)}{150} } }[/tex]

The calculated Z-value = 3.596 > 1.96 at 5% level of significance

Null hypothesis is rejected

Alternative Hypothesis is Accepted

Conclusion:-

The actual percentage of type A donations is not differs from 40%,the percentage of the population having type A blood.

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