Suppose that a researcher wants to estimate a proportion P to within .02 with 95% probability. What is the minimum sample size required?
To find the minimum sample size required to estimate a proportion within a certain margin of error with a specified level of confidence, you can use the formula for sample size calculation for proportions. This formula is based on the normal distribution and is given by:
n = (Z^2 * P * (1-P)) / E^2
Where:
n = required sample size
Z = Z-value corresponding to the desired level of confidence (in this case, for 95% confidence, Z ≈ 1.96)
P = estimated proportion (0.5 is commonly used when the true proportion is unknown)
E = margin of error (0.02 in this case)
Plugging the values into the formula:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.02^2
n = (3.8416 * 0.25) / 0.0004
n = 0.9604 / 0.0004
n ≈ 2401
So, the minimum sample size required to estimate the proportion within 0.02 with 95% probability is approximately 2401.