11.40 Exercise and post hoc tests: Use the same data from the previous exercise in this exercise.

a. Explain why it is necessary to conduct a post hoc test such as a Tukey HSD test when an ANOVA is statistically significant.

b. Conduct a Tukey HSD test. Show all calculations.

c. Explain why we cannot assume that two groups have the same means when we fail to reject the null hypothesis using a Tukey HSD test. Refer to the current example in your answer.