A proportion in a poll
In a sample of 1000 registered voters, 227 say they will vote for a given party. Using the Wald approximation and z_{0.975}=1.960, give an approximate 95% confidence interval for the population proportion.
Worked answer (click to show)
\widehat p=227/1000=0.227. The estimated standard error is
\sqrt{\frac{0.227\times 0.773}{1000}}\approx 0.01325.
The interval is 0.227\pm 1.960\times 0.01325, that is (0.201,\,0.253).