Q:

A random sample of 157 recent donations at a certain blood bank reveals that 86 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? Carry out a test of the appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses.

Accepted Solution

A:
Answer: Yes, this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood.Step-by-step explanation:Since we have given n = 157x = 86So, [tex]\hat{p}=\dfrac{x}{n}=\dfrac{86}{157}=0.55[/tex]and we have p = 0.4So, hypothesis would be [tex]H_0:p=\hat{p}\\\\H_a:p\neq \hat{p}[/tex]Since there is 1% level of significance.So, test statistic value would be [tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.55-0.40}{\sqrt{\dfrac{0.4\times 0.6}{157}}}\\\\z=\dfrac{0.15}{0.039}\\\\z=3.846[/tex]and the critical value at 1% level of significance , z = 2.58Since 2.58<3.846.So, we reject the null hypothesis.Hence, Yes, this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood.