Enter the population standard deviation, confidence level, and desired margin of error to calculate the required sample size to estimate a population mean.
Required Sample Size:
Understanding Sample Size Calculation for Mean
This calculator uses the following formula to determine the sample size required to estimate a population mean within a specified margin of error and confidence level:
$$ n = \frac{{Z^2 \cdot \sigma^2}}{{E^2}} $$
where:
- \( n \) = Sample size
- \( Z \) = Z-score associated with the confidence level
- \( \sigma \) = Population standard deviation
- \( E \) = Margin of error
Real-Life Example: Estimating Average Time Spent on a Website
Suppose a company wants to estimate the average time users spend on their website, with a 95% confidence level and a margin of error of 5 minutes. Based on previous data, they estimate the population standard deviation is 10 minutes.
Here’s the step-by-step calculation:
- Step 1: Set the values: confidence level = 95%, margin of error = 5, standard deviation (σ) = 10.
- Step 2: Find the Z-score for a 95% confidence level (Z ≈ 1.96).
- Step 3: Use the formula:
$$ n = \frac{{(1.96)^2 \cdot (10)^2}}{{(5)^2}} = 15.37 $$
- Interpretation: The company would need a sample size of at least 16 people to estimate the average time within a 5-minute margin of error.