Facts About the F Distribution · Exercise 21

A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are in. Using a 5% significance level, test the hypothesis that the three mean commuting mileages are the same.

$$\begin{array}{ccc}\text{Working-class}& \text{Professional (middle incomes)}& \text{Professional (wealthy)}\\ \text{17.8}& \text{16.5}& \text{8.5}\\ \text{26.7}& \text{17.4}& \text{6.3}\\ \text{49.4}& \text{22.0}& \text{4.6}\\ \text{9.4}& \text{7.4}& \text{12.6}\\ \text{65.4}& \text{9.4}& \text{11.0}\\ \text{47.1}& \text{2.1}& \text{28.6}\\ \text{19.5}& \text{6.4}& \text{15.4}\\ \text{51.2}& \text{13.9}& \text{9.3}\end{array}$$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Business Statistics 2e · §12.4 Facts About the F Distribution · Exercise 21