A random sample of 5000 people was chosen for a survey 54 of

A random sample of 5000 people was chosen for a survey. 54% of them said that they did not have children under 18 living at home.

Find the 95% confidence interval.

Solution

A random sample of 5000 people was chosen for a survey. 54% of them said that they did not have children under 18 living at home. The percentage that had children under 18 living at home is 46%.

The standard deviation is [SD=sqrt(p*(1 - p)*n)] = [sqrt(5000*0.54*0.46)] = [3*sqrt 138 ~~ 35.2420]

The mean is [n*p = 2700]

The 95% confidence interval is [((2700 - (1.96*35.2420)), (2700 + (1.96*0.35.2420)))] = (2630.9256, 2769.0743)

The required 95% confidence interval is (2630.9256, 2769.0743)