A polling agency wants to determine the size of a random sample needed to estimate theproportion of homeowners who keep a hand gun in their home for security. The estimate shouldhave margin of error no more than 2.5 percentage points at a 95% level of confidence. Choose themost conservative answer that is closest to your calculated number, rounding to the nearest wholeperson.
A) They should poll at least 1600 people.
B) They should poll at least 1200 people.
C) They should poll at least 400 people.
D) They should poll at least 1000 people.

Question

Quizplus · Accepted Answer

To find the sample size for a proportion with a given margin of error and confidence level, use the formula n = (Z^2 * p * (1-p)) / E^2. For the most conservative estimate, use p = 0.5. With a 95% confidence level, Z is approximately 1.96, and E is 0.025. Calculating gives n ≈ 1537, so the closest conservative choice is 1600.

A Polling Agency Wants to Determine the Size of a Random