Question

In a survey of 3450 registered voters who reside in California, 1789 were found to be republican. Construct a confidence estimate for the true percentage of republicans among registered voters in California. Use a confidence level of 95%.

Answer 1

Sample size, N = 3450
Point estimate of republican, p = 1789/3450 = 0.5186 = 51.86%
Z = 1.96 at 95% confidence level

Now,
True percentage of republican residing in California = p +/- Z*Sqrt [p91-p)/N] = 0.5186+/- 1.96* Sqrt [0.5186(1-0.5186)/3450] = 0.5186+/-0.017 = (0.5016,0.5356) = (50.16%,53.56%).