Statistics for Two Categorical Variables Practice Test

A university compared two residence types (On-campus vs Off-campus) and surveyed whether students participated in at least one club (Yes/No). The purpose is to compare conditional proportions of club participation by residence type. Based on the two-way table, which comparison is supported?

Two-way table of Residence by Club Participation (proportions of all students):

• On-campus & Yes: 0.35, On-campus & No: 0.15
• Off-campus & Yes: 0.28, Off-campus & No: 0.22

A teacher compared two homework policies (Optional vs Required) and noted whether students turned in the assignment (Turned in/Did not turn in). The purpose is to compare conditional proportions of turning in homework by policy. Based on the two-way table, which comparison is supported?

Two-way table of Policy by Turn-in Status (proportions of all students):

• Optional & Turned in: 0.21, Optional & Did not: 0.29
• Required & Turned in: 0.36, Required & Did not: 0.14