Test the hypothesis using the Pvalue approach Be sure to ver

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.

H0: p=0.3 versus H1: p>0.3

n=200, x=75, a=0.05

(A) is np0 (1-p0) > or equal to 10?

(B) Find the P-value

p-value=___ (Round to three decimal places)

(C) __ the null hypothesis, because the P-value is ____ than a.

Solution

Set Up Hypothesis
Null, H0:P=0.3
Alternate, H1: P>0.3
Test Statistic
No. Of Success chances Observed (x)=75
Number of objects in a sample provided(n)=200
No. Of Success Rate ( P )= x/n = 0.375
Success Probability ( Po )=0.3
Failure Probability ( Qo) = 0.7
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.375-0.3/(Sqrt(0.21)/200)
Zo =2.3146
| Zo | =2.3146
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.315 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 2.31455 ) = 0.01032
Hence Value of P0.05 > 0.01032,Here we Reject Ho

ANS:

a) YES b) 0.01 c) Reject Ho, lessar