A random sample of 144 recent donations at a certain blood bank reveals that 81 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.

Since the p value is very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true percent of people with type A of blood is significantly different from 0.4 or 40%

Step-by-step explanation:

Information given

n=144 represent the random sample taken

X=81 represent the number of people with type A blood

[tex]\hat p=\frac{81}{144}=0.5625[/tex] estimated proportion of people with type A blood

[tex]p_o=0.4[/tex] is the value that we want to verify

[tex]\alpha=0.01[/tex] represent the significance level

z would represent the statistic

[tex]p_v{/tex} represent the p value

Hypothesis to test

We want to test if the percentage of the population having type A blood is different from 40%.:

Null hypothesis:[tex]p=0.4[/tex]

Alternative hypothesis:[tex]p \neq 0.4[/tex]

the statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)

Replacing the info given we got:

[tex]z=\frac{0.5625 -0.4}{\sqrt{\frac{0.4(1-0.4)}{144}}}=3.98[/tex]

Now we can calculate the p value with this probability taking in count the alternative hypothesis:

[tex]p_v =2*P(z>3.98)=0.0000689[/tex]

Since the p value is very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true percent of people with type A of blood is significantly different from 0.4 or 40%