Another nonparametric test known as Tukey’s quick test can be useful with two groups when one group has the minimum value overall (which we call the lower group) and the other (which we call the upper group) has the maximum. The Tukey test works by counting the “exceedences,” the number of observations in the lower group that are less than all the observations in the upper group plus the number in the upper group that are greater than all the observations in the lower group (count ties as 0.5). Call this number E. Then the test rejects the null hypothesis of equal means at α = 0.05 if E ≥ 7, at α = 0.01 if E ≥ 10, and at α = 0.001 if E ≥ 13. Using the data from Exercise 10-36, see whether you come to the same conclusion about the null hypothesis.