(Solution) - Refer to the data in Exercise 11 At -(2025 Original AI-Free Solution)

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Refer to the data in Exercise 11. At ? = 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: 1 versus 2, 1 versus 3, and 2 versus 3. For each comparison, calculate
where a and b 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.