A random sample of 145 recent donations at a certain blood b

A random sample of 145 recent donations at a certain blood bank reveals that 88 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. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the percentage of type A donations differs from 40%. Reject the null hypothesis. There is not sufficient evidence to conclude that the percentage of type A donations differs from 40%. Do not reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%. Reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%. Would your conclusion have been different if a significance level of 0.05 had been used? O Yes (a)

Solution

Set Up Hypothesis
Null, H0:P=0.4
Alternate, H1: P!=0.4
Test Statistic
No. Of Success chances Observed (x)=88
Number of objects in a sample provided(n)=145
No. Of Success Rate ( P )= x/n = 0.6069
Success Probability ( Po )=0.4
Failure Probability ( Qo) = 0.6
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.6069-0.4/(Sqrt(0.24)/145)
Zo =5.0855
| Zo | =5.0855
Critical Value
The Value of |Z | at LOS 0.01% is 2.58
We got |Zo| =5.085 & | Z | =2.58
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 5.08548 ) = 0
Hence Value of P0.01 > 0,Here we Reject Ho

ANS:
Z =5.0855 ~ 5.09
P - Value = 0