If we require a margin of error of x% for the sample size n, express n in terms of x.
To express the sample size, n, in terms of the margin of error, x%, you need to use the formula for sample size calculation, which is based on the desired margin of error and the level of confidence.
Here is the formula:
n = (Z^2 * p * (1 - p)) / (E^2)
Where:
- n is the sample size
- Z is the Z-score associated with the desired level of confidence (usually taken from a standard normal distribution table)
- E is the margin of error expressed as a decimal (E = x/100)
- p is the estimated proportion of the population that has a certain characteristic (if you don't have an estimate, you can use p = 0.5 which provides the largest sample size)
Let's assume you want a margin of error, x%, and a 95% confidence level. In this case, the Z-score is approximately 1.96 (for a 95% confidence level).
Now, you can substitute the values into the formula and calculate n:
n = (1.96^2 * p * (1 - p)) / ((x/100)^2)
Remember to square the Z-score and divide x% by 100 to convert it into a decimal.
This formula will give you the sample size, n, required to achieve the desired margin of error, x%.