The side-by-side box plot displayed reveals an outlier in the group of students taught by method 3 (praised). (Outliers are discussed in Section 1.5.) Verify that 23 is the outlier by showing that it lies outside the interval (Q1 − 1.5 × IQR, Q3 + 1.5 × IQR), where IQR is the interquartile range and Q1, Q3 are the lower and upper quartiles of the arithmetic scores of the students taught by method 3.

(a)    Compute the three treatment means and the grand mean y1., y2., y3., y… (b) Compute SSTr, SSE, and SST, and verify that SST = SSTr + SSE. (c) Construct the ANOVA , and test the null hypothesis, at the 5% level, that there are no significant differences among the three methods of producing the rubber compound.