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 confidiedence interval 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

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=55
Sample Size(n)=100
Sample proportion = x/n =0.55
Confidence Interval = [ 0.55 ±Z a/2 ( Sqrt ( 0.55*0.45) /100)]
= [ 0.55 - 2.58* Sqrt(0.0025) , 0.55 + 2.58* Sqrt(0.0025) ]
= [ 0.4216,0.6784]

We have evidence to support proportion is 0.50