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How do we use the sampling distribution in hypothesis testing? Let's think again about what the sampling distribution shows us. The values used to create the sampling distribution are sample means that we calculated by taking random samples from a known population. Therefore, the sampling distribution shows us the values of the mean we can expect just from taking a smaller sample from a larger population. It is a distribution of expected values. We can then take a single sample and place it on the sampling distribution. This will tell us whether our sample is typical of samples drawn from a population or whether it is unexpected.
Let's do this with the first sample (1, 3, 4, 4, 5) that we drew from the population. The mean of this sample is 3.4.
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