In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is
A) .871 to .929.
B) .120 to .280.
C) .765 to .835.
D) .071 to .129.

Question

Quizplus · Accepted Answer

The proportion of voters not favoring the incumbent is 1 - (360/400) = 0.1 or 10%. Using the formula for a confidence interval for a proportion, p ± Z*(sqrt[p(1-p)/n]), where p is the sample proportion (0.1), n is the sample size (400), and Z is the Z-value for a 95% confidence interval (approximately 1.96), we calculate the confidence interval for the proportion not favoring the incumbent. This calculation yields a confidence interval of approximately 0.071 to 0.129, which corresponds to choice D.

In a Sample of 400 Voters, 360 Indicated They Favor