Refer to the data in Exercise 11. At = 0.10, perform a Scheff Test to determine

Refer to the data in Exercise 11. At α = 0.10, perform a Scheffé Test to determine which means have a significant difference.

In Exercise 11

If the null hypothesis is rejected in a one-way ANOVA test of three or more means, then a Scheffé Test can be performed to find which means have a significant difference. In a Scheffé Test, the means are compared two at a time. For instance, with three means you would have the following comparisons: x̅₁ versus x̅₂, x̅₁ versus x̅₃, and x̅₂ versus x̅₃. For each comparison, calculate

where x̅_a and x̅_b are the means being compared and n_a and n_b are the corresponding sample sizes. Calculate the critical value by multiplying the critical value of the one-way ANOVA test by k - 1. Then compare the value that is calculated using the formula above with the critical value. The means have a significant difference when the value calculated using the formula above is greater than the critical value.

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Northeast Midwest South West 67.6 67.3 68.4 66.2 66.5 68.6 66.6 67.6 65.6 68.9 65.5 68.5 67.4 68.0 64.2 66.1 64.1 67.4 65.8 69.7 66.1 68.5 62.7 65.2 68.0 66.7 63.6 67.1 65.2 68.8 65.2 67.7 64.0 66.6