Final answer:
The correct formula for the standard error of the mean, used for constructing confidence intervals, is the population standard deviation divided by the square root of the sample size for a known population standard deviation, or the sample standard deviation divided by the square root of the sample size when it is unknown.
Step-by-step explanation:
The equation to estimate the standard error of the mean (SEM) for the purpose of constructing confidence intervals and performing statistical inference is neither of the four options provided. However, the correct formula for the SEM when the population standard deviation (o) is known is the population standard deviation divided by the square root of the sample size (n), which can be expressed as o/√n. When o is unknown, and we are using a sample standard deviation (s), the SEM is s/√n. The SEM is then used to construct the confidence interval by taking the sample mean (x) and adding and subtracting the EBM (error bound for a population mean), which is the product of the SEM and the appropriate z-score for the desired confidence level.
For example, if we are working with a 95% confidence level and we know our sample mean (x) and the SEM, we can calculate the EBM using the z-score that corresponds to a 95% confidence level from the z-table. The confidence interval would then be (x - EBM, x + EBM). This interval has a certain level of confidence of containing the true population mean (μ).