To determine which measure describes how much a sample mean varies when different samples are chosen, let's look into each option provided:
A. Sample Mean: The sample mean is the average of the data values in a single sample. It does not describe the variability of the sample means from different samples.
B. Population Mean: The population mean is the average of all the data values in the entire population. It is a fixed value and does not account for any variability among sample means.
C. Standard Error of the Mean: The standard error of the mean (SEM) measures the dispersion or variability of sample means around the population mean. It provides an estimate of how much variation one can expect in sample means if different samples are taken from the same population.
D. Confidence Interval: A confidence interval is a range of values, derived from sample statistics, that is likely to contain the population parameter. It is related to the variability of the sample means but does not directly describe how much the sample mean varies when different samples are chosen.
Given these explanations, the correct answer is:
C. Standard error of the mean
The standard error of the mean specifically addresses the question of how much the sample mean varies when different samples are drawn from the population.
