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

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

The confidence interval is given by

`p \pm z*\sqrt{ (p(1-p))/(n) }`
where z* = 1.96 at the 95% confidence level.


`1.96 \sqrt{ (0.519(1-0.519))/(3450) } = 0.0167`
Therefore the 95% confidence interval is
(0.519 - 0.0167, 0.519 + 0.0167)
= (0.5023, 0.5357)
= (50.2%, 53.6%)

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