Question

A political pollster wants to know what proportion of voters are planning to vote for the incumbent candidate in

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