The estimate of the population proportion is to be within plus or minus 0.06%, with a 99% level of confidence. The best estimate of the population proportion is 0.22. How large a sample is required? Round answer to the next whole number.
To determine the sample size required, we can use the formula for sample size calculation for estimating population proportion:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = z-score corresponding to the desired level of confidence
p = estimated population proportion
E = margin of error
In this case, Z = 2.58 (for a 99% level of confidence, with two-tailed sampling), p = 0.22 (given in the question as the best estimate of the population proportion), and E = 0.06% = 0.0006 (as the desired margin of error).
Substituting the values into the formula:
n = (2.58^2 * 0.22 * (1-0.22)) / 0.0006^2
Simplifying the equation:
n = (6.6564 * 0.22 * 0.78) / 0.00000036
n = 1.3653864 / 0.00000036
n = 3,792,740.44
Rounding up to the next whole number, the required sample size is 3,792,741.