Refer to the data in Exercise 7. At = 0.01, perform a Scheff Test to determine

Refer to the data in Exercise 7. At α = 0.01, perform a Scheffé Test to determine which means have a significant difference.

In Exercise 7

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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