Consider the hypothesis test given by Hop 05 Hp 05 In a rand

Consider the hypothesis test given by

Ho:p= 0.5

H:p> 0.5

In a random sample of 625 subjects, the sample proportion is found to be pˆ=0.55.

(a) Determine the test statistic. Show all work

(b) Determine the P-value for this test. Show all work; writing the correct P-value,

(c) Is there sufficient evidence to justify the rejection of H at the = 0.01 level? Explain.

Solution

Set Up Hypothesis
Null, H0:P=0.5
Alternate, H1: P>0.5
Test Statistic
Number of objects in a sample provided(n)=625
No. Of Success Rate ( P )= x/n = 0.55
Success Probability ( Po )=0.5
Failure Probability ( Qo) = 0.5
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.55-0.5/(Sqrt(0.25)/625)
Zo =2.5
| Zo | =2.5
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =2.5 & | Z | =2.33
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 2.5 ) = 0.00621
Hence Value of P0.01 > 0.00621,Here we Reject Ho

[ANSWER]
a.
Zo =2.5

b.
P-Value: Right Tail - Ha : ( P > 2.5 ) = 0.00621

c.
Yes, there is sufficient evidence to justify the rejection of Ho