Question

Suppose 180 randomly selected people are surveyed to determine whether or not they plan on voting to reelect the current president. Of the 180 surveyed, 36 reported they will not vote to reelect the current president. Identify the values needed to calculate a confidence interval for the proportion that will not vote to reelect the current president at the 99% confidence level. Then find the confidence interval.

Answer 1

(0.123 ; 0.277)

Explanation:

Given :

Sample size, n = 180

x = 36

Proportion, p = x / n = 36/180 = 0.2

Confidence interval for sample proportion :

Confidence interval :

p ± Zcritical * √p(1 - p) / n

Zcritical at 99% = 2.576

0.2 ± 2.576 * √0.2(1 - 0.2) / 180

0.2 ± 2.576 * 0.0298142

0.2 ± 0.0768013792

(0.123 ; 0.277)