Which statement best describes estimated standard error?

Which statement best describes estimated standard error?

• A. It uses the population standard deviation.
• B. It estimates the real standard error when sigma is unknown.
• C. It replaces the sample mean.
• D. It is always equal to the population standard deviation.

Answer: (B)

The standard error of the mean describes how much sample means would vary if you drew repeated samples from the population. If you knew the population standard deviation, you could compute it exactly as sigma divided by the square root of the sample size. But sigma is usually unknown, so we estimate it by using the sample standard deviation, giving an estimated standard error of s divided by the square root of n. This estimated value approximates the true standard error and is what you use for confidence intervals and t-tests when sigma isn’t known. It’s not about replacing the sample mean, and it isn’t generally equal to the population standard deviation; it’s an estimate that gets closer to the true value with larger samples.

The standard error of the mean describes how much sample means would vary if you drew repeated samples from the population. If you knew the population standard deviation, you could compute it exactly as sigma divided by the square root of the sample size. But sigma is usually unknown, so we estimate it by using the sample standard deviation, giving an estimated standard error of s divided by the square root of n. This estimated value approximates the true standard error and is what you use for confidence intervals and t-tests when sigma isn’t known. It’s not about replacing the sample mean, and it isn’t generally equal to the population standard deviation; it’s an estimate that gets closer to the true value with larger samples.