A researcher wishes to estimate the mean weekly wage of the several hundreds of workers employed
by a certain firm within plus or minus 20USD and with a 99% degree of confidence. From past
experience, the researcher knows that the weekly wages of these employees are normally distributed
with a standard deviation of 40USD. What is the minimum sample size required? [
1600
To determine the minimum sample size required to estimate the mean weekly wage with a desired level of precision and confidence, we can use the formula for sample size calculation for estimating the population mean:
n = (Z * σ / E)^2
Where:
- n is the minimum sample size
- Z is the Z-score corresponding to the desired level of confidence
- σ is the standard deviation of the population
- E is the desired margin of error
In this case, the researcher wants to estimate the mean weekly wage within plus or minus 20 USD with a 99% degree of confidence. Given that the standard deviation of the wages is 40 USD, we can plug in these values into the formula and solve for n:
n = (Z * σ / E)^2
n = (2.576 * 40 / 20)^2
n = 5.152^2
n = 26.530304
Therefore, the minimum sample size required is approximately 27.