Question

To develop a confidence interval for the population mean difference, you need to calculate the estimated standard error of the difference of sample means. The estimated standard error is?

Answer 1

To calculate the standard error, follow these steps:

1. Record the number of measurements (n) and calculate the sample mean (μ). This is just the average of all the measurements.
2. Calculate how much each measurement deviates from the mean (subtract the sample mean from the measurement).
3. Square all the deviations calculated in step 2 and add these together:
   Σ(xi - μ)²
4. Divide the sum from step 3 by one less than the total number of measurements (n - 1).
5. Take the square root of the number you got in step 4. This is known as the standard deviation (σ).
6. Finally, divide the standard deviation from step 5 by the square root of the number of measurements (n) to get the standard error of your estimate.

You'll often see these steps expressed as formulas like these, where σ is the standard deviation and SE is the standard error:

Xi_μ steps 1 - 5 : σ n-1 step 6 Vn