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 (season: summer/winter), columns for other (sport: yes/no), cells show counts (36 students: summer AND sport yes). Relative frequencies: row relatives show conditional—of summer students, 36/60=60% play sport vs 16/40=40% of winter students. Different rates (60% vs 40%) suggest association: favorite season relates to playing sports (summer fans more likely). Similar rates suggest independence. The correct comparison uses row relatives 36/60=60% and 16/40=40%, showing summer higher, as in choice B. A common error is using wrong denominators, like grand total in choice A (36/100=36%, 16/100=16%) or inverting fractions in choice C (60/36≈167%, 40/16=250%), leading to incorrect conclusions.

This question tests constructing two-way tables for categorical data, calculating row/column totals, and ensuring the table accurately represents the given frequencies. A two-way table organizes data with rows for one variable (curfew: yes/no) and columns for the other (chores: yes/no), where cells show counts, such as 20 students with curfew and chores. To construct it, identify the variables and categories, count combinations like 20 with curfew and chores, and compute totals, such as row totals of 30 and 20, column totals of 25 each, and grand total of 50. The correct table is the one in choice A, which matches the given data: 20 and 10 for curfew yes, 5 and 15 for curfew no, with accurate totals. A common error is switching cell values, like in choice D where chores yes and no are swapped, leading to incorrect representation. For association, though not directly asked, comparing row relatives (e.g., 20/30 ≈67% vs 5/20=25%) would suggest a link, but focus here on accurate table setup. Mistakes include incorrect totals, like in choice B where row totals are wrong (35 and 15 instead of 30 and 20), or confusing row and column variables as in choice C.

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 interpreting associations in two-way tables by comparing conditional relative frequencies. Association is supported by differing rates, like 20/30≈67% chores among curfew-yes vs 5/20=25% among no-curfew. Data: curfew yes (20 chores,10 no), no (5,15), with unequal conditionals indicating relation. Choice A best supports this using row relatives. Errors: marginals (B:30 vs20), overall (C:25/50=50%), causation (D). Compare relatives across categories—if different, associated. Mistakes include using absolutes or inferring cause.

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 (grade: 6th/8th), columns for other (activity: yes/no), cells show counts (25 students: 6th AND activity yes). To find total not in activity, add the 'no' cells: 15 (6th no) + 10 (8th no) = 25. Construction: identify variables, count combinations, organize in table with totals (e.g., row totals 40 each, column no total 25, grand 80). The correct number is 15+10=25, as in choice D, showing the addition of the relevant cells. A common error is confusing categories, like adding row totals in choice B (40) or grand total in choice C (80), or switching yes/no like in an inverted table. For association, compare row relatives (e.g., 25/40=62.5% vs 30/40=75%), but here focus on extracting totals from described data.

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 (bring lunch: yes/no), columns for other (buy snack: yes/no), cells show counts (18: bring yes AND snack yes). Relative frequencies: row relatives show conditional—of bring lunch students, 18/24=75% buy snack vs 12/36≈33% of no-bring students. Different rates suggest association: bringing lunch relates to buying snacks (bringers more likely). Similar rates suggest independence. The correct set of row relatives is 18/24=75% and 12/36≈33%, as in choice A. A common error is using grand total like in choice B (18/60=30%, 12/60=20%) or inverting like in choice C (24/18=133%, 36/12=300%), or wrong cells like 6/24=25% in choice D (percent not buying).

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, ensuring accurate placement of frequencies and calculation of row/column totals. A two-way table organizes two variables, with rows for one (curfew: yes/no), columns for the other (chores: yes/no), and cells for joint counts, such as 20 for curfew yes and chores yes. Given data: 30 students with curfew (20 with chores, 10 without), 20 without curfew (5 with chores, 15 without), leading to column totals of 25 each and grand total 50. The correct table is choice A, matching all joint frequencies, row totals (30 and 20), column totals (25 and 25), and grand total 50. Common errors include incorrect cell values or totals, like B's inflated curfew yes total of 35, C's mismatched cells after switching rows/columns, or D's wrong no-curfew counts and grand total of 45. Construction steps: (1) identify variables and categories, (2) place given joint counts in cells, (3) sum for row and column totals, (4) add grand total to verify. Mistakes often arise from misreading data or arithmetic errors in summing.

This question tests constructing two-way tables for categorical data, calculating row/column relative frequencies (percentages), and identifying associations by comparing conditional rates. Tables use rows for one variable (e.g., housing: apartment/house) and columns for another (pet: yes/no), with cells for counts like 15 apartments with pets, and totals like 50 apartments, 55 pets. Relatives might show 15/50 = 30% of apartments have pets vs 40/50 = 80% of houses, differing rates suggesting association, similar implying independence. For 100 families (apartment: 15 yes, 35 no, total 50; house: 40 yes, 10 no, total 50; totals yes 55, no 45), choice A correctly fills the table with accurate counts and totals. Errors: wrong totals (B), swapped cells (C), incorrect counts (D). Construction: (1) identify categories, (2) place counts, (3) sum rows/columns, (4) grand total. Mistakes: switching values or misadding.

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.