Question

The Atlanta Journal Constitution conducted a survey of 900 registered voters to determine which voting method they prefer. The AJC found 60% favored voting on paper ballots they filled themselves (as opposed to voting with a computer). Find a confidence interval for the proportion of all registered voters that favor at 85% confidence level. a) (0.576, 0.624) b) (0.376, 0.424) c) (0.583, 0.617) d) (0.586, 0.614)

Answer 1

a) (0.576, 0.624)

Explanation:

Given that the sample proportion (p) = 60% = 0.6, sample size (n) = 900, confidence (C) = 85%

α = 1 - C = 1 - 0.85 = 0.15

α/2 = 0.075

The z score of α/2 (0.075) corresponds with the z score of 0.425 (0.5 - 0.075) which is equals to 1.44, hence
`z_(\alpha )/(2) =1.44`

The margin of error (E) is:

`E=z_(\alpha )/(2) *\sqrt{(p(1-p))/(n) } =1.44*\sqrt{(0.6(1-0.6))/(900) } = 0.024`

The confidence interval = p ± E = 0.6 ± 0.024 = (0.576, 0.624)