Question

In a​ poll,69 ​% of the people polled answered yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?" The margin of error in the poll was ​3%, and the estimate was made with ​96% confidence. At least how many people were​ surveyed?

Answer 1

At least 291 people were surveyed.

Step-by-step explanation:

To find out how many people were surveyed, we can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

• n is the sample size
• Z is the z-score corresponding to the confidence level, which is 2.053 for a 96% confidence level
• p is the proportion of people who answered yes, which is 0.69
• E is the margin of error, which is 0.03

Substituting the values, we have:

n = (2.053^2 * 0.69 * (1 - 0.69)) / 0.03^2

n = (4.215 × 0.69 × 0.31) / 0.0009

n ≈ 290.11

Rounding up, at least 291 people were surveyed.