2. The F distribution is used to construct a one-way ANOVA test for comparing several sample means.

(a) Outline the basic purpose of ANOVA. How does ANOVA avoid high risk due to multiple type I errors?

(b) Outline the basic assumption for ANOVA.

(c) What are the null and alternate hypotheses in an ANOVA test? If the test conclusion is to reject the null hypothesis, do we know which of the population means are different from each other?

(d) What is the F distribution? How are the degrees of freedom for numerator and denominator determined?

(e) What do we mean by a summary table of ANOVA results? What are the main components of such a table? How is the final decision made?