Confidence interval T table

Question

Out of 600 people sampled, 54 preferred Candidate A. Based on this, estimate what proportion of the voting population () prefers Candidate A.

Use a 99% confidence level, and give your answers as decimals, to three places.

 ______<  < _______

Answer 1

sample proportion phat = 54/600 = 0.09

sample size (n) = 600

since 99% CI is middle 0.99 proportion of area, leaving 0.005 of area on each tail, z-critical is z-score for probability = 0.995 = 2.575

CI = phat +/- z-critical * sqrt(phat*(1-phat)/n)

CI = 0.09 +/- 2.575 * sqrt(0.09*0.91/600)