The Student Activities Board (SAB) at a liberal arts college wants to study the effect of participation in extracurricular activities on students’ GPA. The SAB draws a random sample of students at its school and asks each respondent for two pieces of information: whether they participate in any extracurricular activities and their GPA.

a. Give the null and alternative hypotheses for an ANOVA test of the relationship between these variables.

b. Give the null and alternative hypotheses for a two-sample test of the relationship between these variables (see chapter 10 for a reminder).

c. Are the hypotheses described in Parts a and b equivalent?