Question

A political pollster wants to know what proportion of voters are planning to vote for the incumbent candidate in
an upcoming election. A poll of 150 randomly selected voters is taken from the more than 2,000 voters in the
population, and 78 of those selected plan to vote for the incumbent candidate.
Based on this sample, which of the following is a 90% confidence interval for the proportion of all voters who
plan to vote for the incumbent candidate?

Answer 1

Answer:

90% confidence interval -> {0.4529, 0.5871}

Step-by-step explanation:

Check conditions for a 1-proportion z-interval:

np>10 -> 150(0.52)>10 -> 78>10 √

n(1-p)>10 -> 150(1-0.52)>10 -> 72>10 √

Random sample √

n>30 √

For a 90% confidence interval, the critical value is z=1.645

The formula for a confidence interval is:

CI = p ± z√[p(1-p)/n]

Given:

p = 78/150 = 0.52

n = 150

z = 1.645

Therefore, the 90% confidence interval is:

CI = 0.52 ± 1.645√[0.52(1-0.52)/150] = {0.4529, 0.5871}

Context: We are 90% confident that the true proportion of all voters who

plan to vote for the incumbent candidate is contained within the interval