A polling agency wants to determine the size of a random sample needed to estimate the proportion of homeowners who keep a hand gun in their home for security. The estimate should have margin of error no more than 2.5 percentage points at a 95% level of confidence. Choose the most conservative answer that is closest to your calculated number, rounding to the nearest whole person.
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, use the formula for margin of error in proportion: ME = Z * sqrt(p(1-p)/n). For the most conservative estimate, use p = 0.5. At 95% confidence, Z is approximately 1.96. Solving for n with ME = 0.025 gives n ≈ 1537.76, so rounding up, they should poll at least 1600 people.

A Polling Agency Wants to Determine the Size of a Random