A study found that 82% of elementary students buy lunch at school at least once a month. How large a sample would be necessary to estimate the true proportion within four percentage points with 95% confidence
n = (z/2 )^2 * pq/E^2
n = (1.96)^2 *0.82*0.18/0.04^2
n = ?
zero is the answer
To determine the sample size needed to estimate the true proportion within a certain margin of error with a specified confidence level, we can use the formula for sample size calculation:
n = (Z^2 * p * (1 - p)) / E^2
Where:
- n is the required sample size
- Z is the desired z-score corresponding to the confidence level
- p is the estimated proportion
- E is the desired margin of error
In this case, we want to estimate the true proportion within four percentage points with 95% confidence. Therefore, the margin of error (E) would be 4 percentage points, translated into a decimal (0.04). The confidence level corresponds to a z-score of 1.96.
Substituting these values into the formula, we have:
n = (1.96^2 * 0.82 * (1 - 0.82)) / 0.04^2
Calculating this will give us the required sample size.