A random sample of 163 recent donations at a certain blood b

A random sample of 163 recent donations at a certain blood bank reveals that 82 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.

H₀: p = 0.40
H_a: p < 0.40H₀: p = 0.40
H_a: p > 0.40    H₀: p 0.40
H_a: p = 0.40H₀: p = 0.40
H_a: p 0.40

State the rejection region(s). If the critical region is one-sided, enter NONE for the unused region. Round your answers to two decimal places.

Compute the test statistic value. Round your answer to two decimal places.
z =  

State the conclusion in the problem context.

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%.Do not reject the null hypothesis. There is not 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?

YesNo    

Solution

Set Up Hypothesis
Null, H0:P=0.4
Alternate, H1: P!=0.4
Test Statistic
No. Of Success chances Observed (x)=82
Number of objects in a sample provided(n)=163
No. Of Success Rate ( P )= x/n = 0.5031
Success Probability ( Po )=0.4
Failure Probability ( Qo) = 0.6
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.50307-0.4/(Sqrt(0.24)/163)
Zo =2.686
| Zo | =2.686
Critical Value
The Value of |Z | at LOS 0.01% is 2.58
We got |Zo| =2.686 & | 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 != 2.68602 ) = 0.00723
Hence Value of P0.01 > 0.0072,Here we Reject Ho

ANS:
z    -2.58
z 2.58
Z = 2.69
Reject the null hypothesis. There is sufficient evidence to conclude that
the percentage of type A donations differs from 40%
No