Question

select the correct answer.

which measure describes the standard error of the mean?

the central limit theorem
the sample mean
the standard deviation of the means
the confidence interval

Explanation:

Define standard error of the mean

The standard error of the mean (SEM) measures the dispersion of sample means around the population mean. It is mathematically defined as the standard deviation of the sampling distribution of the sample mean.

Evaluate the given options

• the central limit theorem: A theorem describing the shape and properties of the sampling distribution, not a measure itself.
• the sample mean: A point estimate of the population mean, not a measure of its variability.
• the standard deviation of the means: This directly corresponds to the definition of the standard error of the mean.
• the confidence interval: An interval estimate of a population parameter, not a single measure of standard error.

Select the correct option

The measure that describes the standard error of the mean is the standard deviation of the means.

Answer:

• the central limit theorem
• the sample mean
• the standard deviation of the means (Correct answer)
• the confidence interval