and second-year students. The following table gives the counts of classes by department, class size {small or large), and students audience. Size Department Year W Total A First 2 0 2 Second 9 1 10 Third 5 15 20 Fourth 4 16 20 B First 18 2 20 Second 40 10 50 Third 4 16 20 Fourth 2 14 16 (a) First, consider only those classes in which the student audience was rst or second year students. Find the conditional proportions that the class size was large for Department A and Department B, respectively. Was a class offered by Department A or B more likely to be large in size when the student audience was rst-year or second-year students? (b) Repeat (a) for classes in which the student audience was third or fourth year students. Was a class offered by Department A or B more likely to be large in size when the student audience was third-year or fourth-year students? (c) Now add these two tables together to get a summary contingency table that describes the association between the class size being large and the department which it was offered, ignoring the information about the student audience. What proportion of Department A's classes are large? What proportion of Department B's classes are large? Which proportion is higher? ((1) How can you explain the association in part (c), whereby classes offered by Department B were more like to be large in size? Why can this association be so different from the ones you found in part (a) and (b)? Hint: Your explanation must address the following. i. When the student audience was first-year or second-year students, was the class size more likely to be large or small? ii. When the student audience was third-year or fourth-year students, was the class size more likely to be large or small? iii. Comparing with classes offered to the third-year and fourth-year students, was a large class or small class more likely to be offered to first-year or second-year students, or no apparent difference? in. Which department offered more classes for third-year or fourth-year students? Use the three observations above to explain how the association in (c) is so different from in the one in part (a) and (h). 5. In each of the following situations, identify the sampling method as one of the following: simple random sampling, stratified sampling, multistage sampling, or voluntary response sampling. (a) There are seven sections of an introductory statistics course. A random sample of three sections is chosen and then random samples of 8 students from each of these sections are chosen. (b) An online poll asks people who visit this site to choose their favorite television show. (c) Separate random samples of rst-year, second-year, third-year, and fourth-year college students in a statistical course are selected to receive a one-week alternate instructional method