Think of drawing several samples of 10 from a population from of 5,000. The population mean (average) is 4.0. The sample means (averages) probably will not be exactly 4.0. A few might be 4.0, but other sample means will fluctuate due to chance. Some samples may have M = 3.97, or M = 4.06, etc. They will vary around the true population mean of 4.

The research question is whether the difference observed between sample means is greater than would be expected by chance (e.g., M = 2.3 versus M = 5.4 in the above situation).

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