Hypothesis testing with one sample Amoung 100 babies born to

Hypothesis testing with one sample:

Amoung 100 babies born to 100 couples using a gender -selection method, 55 of them are girls. Use a 0.01 significance level to test the claim that for couples using this method, the proportion of girls is not equal to 0.5.

Use the classical/ traditional approach to solve-

Solution

Set Up Hypothesis
Null, H0:P=0.5
Alternate, the proportion of girls is not equal to 0.5 H1: P!=0.5
Test Statistic
No. Of Success chances Observed (x)=55
Number of objects in a sample provided(n)=100
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)/100)
Zo =1
| Zo | =1
Critical Value
The Value of |Z | at LOS 0.01% is 2.58
We got |Zo| =1 & | Z | =2.58
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 1 ) = 0.31731
Hence Value of P0.01 < 0.3173,Here We Do not Reject Ho