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.
