Calculate the minimum sample size required to find the 90% interval estimate for a population proportion if you want to be accurate within 2%.
To calculate the minimum sample size required to find a desired interval estimate for a population proportion with a specified level of accuracy, you can use the following formula:
n = (Z^2 * p * (1-p)) / E^2
where:
- n represents the sample size,
- Z is the critical value corresponding to the desired level of confidence (in this case, 90%, so Z = 1.645),
- p is the estimated proportion of the population,
- (1-p) is the complementary probability of p,
- E is the desired level of accuracy (in this case, 2%).
To apply this formula, you need to estimate the population proportion (p). If you do not have an estimate, you can use 0.5, which provides the maximum sample size needed under the assumption of maximum variance.
Let's calculate the minimum sample size required:
n = (1.645^2 * 0.5 * (1-0.5)) / 0.02^2
n = (2.705 * 0.25) / 0.0004
n = 1.3525 / 0.0004
n ≈ 3381.25
So, the minimum sample size required to obtain a 90% interval estimate for a population proportion with an accuracy of within 2% is approximately 3381.