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

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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 x̅a and x̅b are the means being compared and na and nb 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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