The formula to determine the mean critical value is as follows:

For our example, μ = 6.0, σ = 2.0, n = 30, and z_cv = -1.645. Let's do the calculations:

This tells us that any sample mean of 5.40 or below is considered extreme (far from the population mean of 6.0), and we will reject the null hypothesis.

Next, we need to work with the alternative hypothesis sampling distribution.