You want to obtain a sample to estimate a population mean age of the incoming fall term transfer students. Based on previous evidence, you believe the population standard deviation is approximately σ=7.2
You would like to be 99% confident that your estimate is within 2 of the true population mean. How large of a sample size is required?
n =
To determine the required sample size, we can use the formula for the sample size formula for estimating a population mean:
n = (Z * σ / E)^2
Where:
n = required sample size
Z = Z-score corresponding to the desired confidence level (99%)
σ = population standard deviation
E = margin of error
Given that the population standard deviation is σ = 7.2 and the desired margin of error is E = 2, we need to find the Z-score for a 99% confidence level.
Using a Z-table or a statistical software, we find that the Z-score corresponding to a 99% confidence level is approximately 2.576.
Plugging in the values into the formula:
n = (Z * σ / E)^2
n = (2.576 * 7.2 / 2)^2
n = (18.5472 / 2)^2
n = 9.2736^2
n = 86.0106
Rounding up to the nearest whole number, the required sample size is 87.