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%.

Given:
n = 3450, sample size
p = 1789/3450 = 0.519 = 51.9%, proportion
Confidence level = 95%

The confidence interval is given by

where z* = 1.96 at the 95% confidence level.


Therefore the 95% confidence interval is
(0.519 - 0.0167, 0.519 + 0.0167)
= (0.5023, 0.5357)
= (50.2%, 53.6%)

At the 95% confidence level, the interval for the proportion is about (50%, 54%).