When we test a hypothesis, we draw a sample from a population, calculate a statistic on the sample, and use this statistic to determine whether the sample came from a known population (null) or a different population (alternative).

Let's look at our sample again.

We drew five scores. The sample mean is 3.4, and the standard deviation is 1.52. We know that this sample came from a defined population (μ = 5.0; σ = 2.0) because we drew the sample.

If you did not see the sampling process yourself, would you think that a sample with a mean of 3.4 came from a population with a mean of 5.0?