Final answer:
The estimated standard error for the sample mean, given a sample size of 100 and a population variance of 400, is calculated to be 2.
Step-by-step explanation:
The student's question involves finding the estimated standard error for the sample mean when given a sample size (n=100) and a population variance (σ2=400). The standard error of the mean is calculated using the formula SE = σ / √n, where σ is the population standard deviation, and n is the sample size.
Since the population variance is given as 400, the population standard deviation (σ) becomes the square root of 400, which is 20. Thus, the estimated standard error (SE) for the sample mean is 20/ √100, which simplifies to 20/10 or 2.
To estimate the standard error for the sample mean, we need to use the formula: Standard Error = Standard Deviation / √n. In this case, the standard deviation is given as 20 and the sample size is 100. So, the estimated standard error for the sample mean is:
Estimated Standard Error = 20 / √100 = 2