Final answer:
To determine the sample size needed to construct a 99% confidence interval to estimate a population proportion, you can use the formula: n = (Z^2 * p * (1-p)) / E^2
Step-by-step explanation:
To determine the sample size needed to construct a 99% confidence interval to estimate a population proportion, you can use the formula:
n = (Z^2 * p * (1-p)) / E^2
where:
- n is the required sample size
- Z is the Z-value for the desired confidence level
- p is the estimated population proportion
- E is the margin of error
Substituting the given values into the formula:
n = (Z^2 * 0.39 * (1-0.39)) / 0.057^2
Once you know the Z-value for a 99% confidence level, you can calculate the required sample size.