For some data sets, the F statistic will reject the null hypothesis of no difference in mean yields, but the Tukey–Kramer method will not find any pair of means that can be concluded to differ. For the four sample means given in Exercise 14, assuming a sample size of 4 for each treatment, find a value of MSE so that the F statistic rejects the null hypothesis of no difference at the 5% level, while the Tukey–Kramer method does not find any pair of means to differ at the 5% level.

Exercise 14.

In an experiment to determine the effect of curing time on the compressive strength of a certain type of concrete, the mean strengths, in MPa, for specimens cured for each of four curing times were X̅₁. = 1316, X̅_2. = 1326, X̅_3. = 1375, and X̅_4. = 1389. Assume that four specimens were cured for each curing time.