A One-Way ANOVA Is to Be Performed $\overline { x _ { 1 } } = 20 , \overline { x _ { 2 } } = 30 , \overline { x _ { 3 } } = 40$

Essay

A one-way ANOVA is to be performed. The following sample data are obtained. $\overline { x _ { 1 } } = 20 , \overline { x _ { 2 } } = 30 , \overline { x _ { 3 } } = 40$ The common population standard deviation for the three populations is 2.5. Do you think that the difference between the sample means could be due to variation within the populations or does it seem clear that the difference between the sample means is due to a difference between population means? Do you think that the null hypothesis would be rejected? Explain your thinking.