This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. Row relatives show conditionals like 15/50 = 30% of apartments have pets versus 40/50 = 80% of houses, the large difference suggesting association between housing and pets, while equal rates indicate independence. For 100 families (equal 50 each housing), choice B correctly states association by comparing row relatives (30% vs 80%) without causation. This fits the conditional analysis. Errors: no association from equal totals (A), irrelevant sums (C), causation claim (D). Association via comparing relatives across rows. Mistakes: overlooking conditionals or confusing with cause.

This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. Row relatives show conditionals like 20/30 ≈ 67% of curfew students have chores versus 5/20 = 25% without, with the difference (67% vs 25%) suggesting association between curfew and chores, as similar rates would indicate independence. In this 50-student example, comparing row relatives (67% vs 25%) shows a higher percentage with curfew have chores, indicating association without claiming causation, as in choice B. This is the correct interpretation based on conditional rates. Errors include ignoring conditionals by using grand totals (20/50 and 5/50 in A), misinterpreting balanced totals as independence (C), or claiming causation (D). For association: compare row relatives across rows (differing suggests related variables). Mistakes: not comparing conditionals or confusing association with causation (association shows correlation, not cause).

This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. Tables organize variables like preference (fiction/nonfiction) and reading time (20+ yes/no), with cells e.g., 18 fiction and 20+, totals enabling relatives like 18/30 = 60% of fiction preferers read 20+ vs 10/30 ≈ 33% nonfiction, difference suggesting association, similarity independence. For 60 students (fiction: 18 yes, 12 no, total 30; nonfiction: 10 yes, 20 no, total 30), total reading 20+ is column sum 18+10 = 28, as in B. This correctly adds the relevant cells. Errors: single cell (18 in A), wrong sum (30 in C), grand total (60 in D). Construction: fill cells, sum columns for totals like reading yes. Mistakes: adding incorrect cells or confusing variables.

This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. Row relatives are conditional, like for houses (50 total), 40/50 = 80% have pets versus 15/50 = 30% for apartments, differences suggesting association, similarity meaning independence. In this 100-family survey (house: 40 pets, 10 no), the row relative for pets in houses is 40/50 = 80%, as in B, using row total. This correctly conditions on housing type. Errors: grand total (40/100 = 40% in A), column total (40/55 ≈ 73% in C), inverted (50/40 = 125% in D). Calculate by dividing cell by row total; compare for association. Mistakes: wrong denominator or miscalculation.

This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. Relative frequencies include row relatives, which show conditional probabilities, such as among students with curfew (30 total), 20/30 ≈ 67% have chores, versus 5/20 = 25% for those without curfew, with differing rates suggesting an association between curfew and chores, while similar rates would indicate independence. In this example with 50 students, the row relative frequency for chores among curfew students is 20/30 ≈ 67%, as calculated in choice B, using the row total as the denominator for the conditional percentage. This is the correct interpretation, as it focuses on the proportion within the curfew-yes row. A common error is using the wrong denominator, like the grand total (20/50 = 40% in A) or column total (20/25 = 80% in C), which computes a different relative frequency. To calculate row relatives: divide the cell count by its row total (e.g., 20/30 for curfew yes and chores yes); for association, compare these across rows. Mistakes include confusing row with column relatives or arithmetic errors, such as misdividing (e.g., treating 30/50 = 60% as the row relative in D).

This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. Row relatives indicate conditionals, such as 30/40 = 75% of 8th graders participate versus 25/40 = 62.5% of 6th graders, with the 12.5% difference suggesting association between grade and participation, while equal rates imply independence. For this 100-student survey (totals: 6th 40, 8th 40), choice A correctly identifies association by comparing row relatives (75% vs 62.5%) without causation. This matches the data's conditional rates. Errors: claiming no association from equal group sizes (B), using grand totals (25/100, 30/100 in C), or causation (D). For association: compare relatives across rows (differences suggest relation). Mistakes: ignoring conditionals or equating association with cause.

This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. Row relatives are conditional, like for 8th graders (40 total), $30/40 = 75%$ participate in activities versus $25/40 = 62.5%$ for 6th graders, with differences suggesting association, while similarity means independence. Here, with 100 students (6th: 25 participate, 15 not, total 40; 8th: 30 participate, 10 not, total 40), the row relative for 8th graders participating is $30/40 = 75%$, as in B. This uses the correct row total denominator for the conditional percentage. Common errors: using grand total ($30/100 = 30%$ in A), inverting fraction ($40/30 \approx 133%$ in C), or wrong row total ($30/55 \approx 55%$ in D, perhaps miscounting). To calculate: divide cell by row total ($30/40$); compare for association. Mistakes include wrong denominators or arithmetic slips.

This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. Relative frequencies include column relatives, which are conditional, such as among students with chores (25 total), 20/25 = 80% have curfew versus 10/25 = 40% without chores, with differences suggesting association, while similarity implies independence. For this 50-student survey, the column relative frequency of curfew among chores students is 20/25 = 80%, as in choice C, using the column total as the denominator. This correctly answers the question by conditioning on the chores-yes column. Errors often involve wrong denominators, like row total (20/30 ≈ 67% in A) or grand total (20/50 = 40% in B). To compute column relatives: divide cell by column total (e.g., 20/25); compare across columns for association. Common mistakes: mixing row/column (e.g., 25/50 = 50% in D) or not recognizing conditional nature.

This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. A two-way table organizes data with rows for one variable (e.g., curfew: yes/no) and columns for the other (e.g., chores: yes/no), where cells show joint frequencies like 20 students with curfew and chores. Relative frequencies include row relatives, which are conditional probabilities, such as 20/30 ≈ 67% of students with curfew having chores compared to 5/20 = 25% without curfew, indicating an association if rates differ substantially, while similar rates suggest independence. For this survey of 50 students, the table should have rows for curfew (yes: 20 chores yes, 10 no, total 30; no: 5 yes, 15 no, total 20) and columns for chores, with totals 25 yes, 25 no, and grand total 50, matching choice D. Common errors include switching row and column variables (as in A), miscalculating totals (as in B), swapping cell values (as in C), or incorrect cell counts. To construct the table: (1) identify variables (curfew yes/no, chores yes/no), (2) fill cells with given counts (e.g., curfew yes and chores yes: 20), (3) add row and column totals (e.g., curfew yes total: 30), (4) verify grand total (50). Mistakes often involve confusing row/column assignments or arithmetic errors in totals, but here D correctly represents the data without such issues.

This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. Two-way table: rows for one variable (housing: apartment/house), columns for other (pet: yes/no), cells show counts (15: apartment yes). Relative frequencies: row relatives show conditional—of apartment families, 15/50=30% have pets vs 40/50=80% of house families. Different rates (30% vs 80%) suggest association: housing type relates to pet ownership (houses more likely). Similar rates suggest independence. The correct conclusion is association due to differing rates, as in choice B, without claiming causation. A common error is claiming causation like in choice C, or misinterpreting equal row totals as no association in choice A.