Question

a tv news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of likely voters indicated that 55% would vote in favor. the reporter goes on to say that the margin of error for this poll was 4% at a confidence level of 95%. what was the sample size?

Answer 1

The sample size can be calculated using the formula: n = (Z^2 * p * (1-p)) / E^2.

Given that the proportion from the poll is 0.55 and the margin of error is 0.04, the sample size is approximately 600.

Step-by-step explanation:

The sample size can be calculated using the formula:

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

Where:

• n is the sample size
• Z is the Z-score corresponding to the desired confidence level
• p is the proportion from the poll
• E is the margin of error

Given that the proportion from the poll is 0.55 and the margin of error is 0.04, we can substitute these values into the formula:

n = (1.96^2 * 0.55 * (1-0.55)) / 0.04^2

n=600

Solving for n, we get a sample size of approximately 600.