political survey 43% of 300 republicans feel gov.has to much power. find 95% confidence

Question

43% of 300 republicans surveyed said gov. has too much power. find the 95% confidence interval.

Answer 1

The proportion p=0.43, so 1-p=0.57 and with n=300 we can find the standard error=sqrt(0.43*0.57/300)=0.02858. The confidence level is 95% so a=1-0.95=0.05. The critical probability is 1-a/2=1-0.025=0.975. This corresponds to a z-score of 1.96 (from the normal distribution table) which, when multiplied by the standard error, gives us the error margin=1.96*0.02858=0.056.

Applying this margin to the proportion of people 0.43 gives us 0.43+0.056 or 43%+5.6% or 37.4%<43%<48.6%.