Question

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.

Answer 1

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 = 157

x = 86

So, $\hat{p}=\dfrac{x}{n}=\dfrac{86}{157}=0.55$

and we have p = 0.4

So, hypothesis would be

$H_0:p=\hat{p}\\\\H_a:p\neq \hat{p}$

Since there is 1% level of significance.

So, test statistic value would be

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.55-0.40}{\sqrt{\dfrac{0.4\times 0.6}{157}}}\\\\z=\dfrac{0.15}{0.039}\\\\z=3.846$

and the critical value at 1% level of significance , z = 2.58

Since 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.