Question

You are running a political campaign and wish to estimate, with a 95% confidence, the proportion of registered voters who will vote for your candidate. Your estimate must be accurate within 3% of the true population. Find the minimum sample size needed when no preliminary estimate is available.

Answer 1

The minimum sample size needed to estimate the proportion of registered voters with 95% confidence and a margin of error no greater than 3% is approximately 1067.

Step-by-step explanation:

To calculate the minimum sample size needed to estimate the proportion of registered voters, we can use the formula:

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

Where:

• n is the minimum sample size
• Z is the Z-score corresponding to the desired confidence level (in this case, 95% confidence corresponds to a Z-score of approximately 1.96)
• p is the estimated proportion of registered voters (since no preliminary estimate is available, we can use 0.5 as a conservative estimate)
• E is the desired margin of error (in this case, 3% or 0.03)

Plugging in the values:

n = (1.96^2 * 0.5 * (1-0.5)) / (0.03^2)

Solving this equation gives us a minimum sample size of approximately 1067. Hence, you would need to interview at least 1067 registered voters to estimate the proportion with 95% confidence and a margin of error no greater than 3%.