Chapter 9.2, Problem 13E

In an experiment to determine the effect of catalyst on the yield of a certain reaction, the mean yields for reactions run with each of four catalysts were ${\bar{X}}_1=89.88$, ${\bar{X}}_2=89.51$, ${\bar{X}}_3=86.98$, and ${\bar{X}}_4=85.79$. Assume that five runs were made with each catalyst.

1. a. If MSE = 3.85, compute the value of the F statistic for testing the null hypothesis that all four catalysts have the same mean yield. Can this null hypothesis be rejected at the 5% level?
2. b. Use the Tukey–Kramer method to determine which pairs of catalysts, if any, may be concluded to differ at the 5% level.