If n=380 and phat=0.25, construct a 95% confidence interval

Answer 1

The confidence interval can be calculated using the equation p +/- z * s.e.(p) where s.e. is the standard error of the sample found from the equation ((1-p)p/n)^(1/2). So we can calculate the standard error to be (.25(0.75)/380)^(1/2) = 0.0222. Our z value for the 95% confidence interval is 1.96 so our confidence interval will be 0.25 +/- 1.96(0.0222) = (0.206, 0.294).