Question

A public opinion poll is taken a week prior to the election of the state governor. There are two candidates, A and B. A random sample is taken among likely voters, and among those people polled, 724 prefer candidate A, and 831 candidates prefer candidate B.

A) Find the 95% confidence interval for the percentage of support of candidate A among likely voters.

B) Find the 95% confidence interval for the percentage of support of Candidate B among likely voters.

C) Is the difference between the two candidates statistically significant at this confidence level? Explain.

Answer 1

a) Total sample size = 724 + 831 = 1555

For candidate A,

Sample proportion = 724/1555 = 0.466

For 95% confidence, z = 1.96

Hence,

95% confidence interval for population percentage of support of candidate A will be:

$0.466 \pm 0.025$

(0.441, 0.491)

(44.1%, 49.1%)

b) 95% confidence interval for percentage of candidate in B's support will be:

(100% - 49.1%, 100% - 44.1%)

(51.9%, 55.9%)

c) Yes, the difference is statistically significant because candidate B is having percentage entirely above 50% and hence, having significantly greater odds of winning as compared to candidate A.