Problem:

In a certain city, there are 100,000 persons aged 21 to 28. 
You do not know the true proportion of married individuals in 
this age group within this city. 

Suppose that a sample of size 400 was drawn that contained 240 
married individuals. 

a) Estimate the true proportion of married individuals aged 21 to 
28 in this city.

b) Compute an error for your estimate.

c) Give a 95% confidence interval for the proportion of married 
individuals aged 21 to 28 in this city.

d) Interpret the 95% CI.



Solution:

a) Estimate of true proportion = 240/400=0.6

b) SD(p)=sqrt(p*(1-p)/n)=sqrt(0.6*0.4/400)=0.0245

c) The z value for 95% is 1.95 hence the 95% CI is p plus/minus 1.95*SD(p).
From above, p is 0.6 and SD(p) is 0.0245. The 95% CI is therefore 
0.6 plus/minus 1.95*0.0245. That is [0.55, 0.65].

d) Given the sample we are 95% confident that the interval [0.55, 0.65] 
containsthe true proportion of married individuals between 21 and 28 in 
the city.