Conditional relative frequency calculates the proportion within a conditioned subgroup, here preferring theater given no streaming subscription. The denominator is the subgroup total for no streaming (80 students). Locate the cell for no streaming and prefer theater (56 students) and the subgroup total (80). Compute the frequency as 56 divided by 80, which equals 0.70 or 70%. A common misconception is using the column total (78) instead of the row, which would incorrectly give 56/78 ≈ 71.8%. To transfer this strategy, interpret 'given that the student does not have a streaming subscription' as using the no streaming total (80) as the denominator, then divide the relevant cell (56) by it to build the ratio.

Conditional relative frequency finds the proportion preferring weekends given involvement in student government. The denominator is the subgroup total for student government yes (60 students). Locate the cell for yes and prefer weekends (42 students) and the subgroup total (60). Compute the frequency as 42 divided by 60, which equals 0.70. A common misconception is using the column total (77) instead, which would give 42/77 ≈ 0.545. To transfer this strategy, translate 'given that the student is involved in student government' to use the yes total (60) as denominator, then divide the relevant cell (42) by it for the ratio.

Joint relative frequency represents the proportion of the total sample that falls into the intersection of two categories, such as having a part-time job and doing homework at the library. The denominator is the overall total (150 students). Locate the cell at the intersection of part-time job yes and homework at library (45 students) and the grand total (150). Compute the frequency as 45 divided by 150, which equals 0.30. A common misconception is confusing joint with conditional frequency by using a row or column total (like 75) instead, which would give 45/75 = 0.60. To transfer this strategy, identify the joint as the specific cell divided by the grand total to find the overall proportion.

Association is assessed by comparing conditional relative frequencies across groups to determine if sports preference differs based on team participation. Calculate conditional frequencies using subgroup totals: for on team, prefer team sports is 48/60 = 0.80; for not on team, it's 30/90 ≈ 0.333. Locate cells for prefer team sports in each group (48 and 30) and divide by group totals (60 and 90). The computation shows students on a team have a higher proportion preferring team sports (80%) than those not on a team (33.3%), implying an association between participation and preference. For association, compare these conditional frequencies across groups; a substantial difference indicates the variables are related. A common misconception is basing association on total counts, like more not on team overall, rather than proportions within groups. To transfer, compute ratios within each row total and compare to see if preferences vary by group.

Conditional relative frequency determines the proportion arriving on time given skipping breakfast. The denominator is the subgroup total for skips breakfast (80 students). Locate the cell for skips and on time (30 students) and the subgroup total (80). Compute the frequency as 30 divided by 80, which equals 0.375 or 37.5%. A common misconception is using the on time column total (100) instead, giving 30/100 = 30%. To transfer this strategy, interpret 'given that the student skips breakfast' as using the skips total (80) as denominator, then divide the relevant cell (30) by it for the ratio.

Association in two-way tables is determined by comparing conditional relative frequencies across groups to see if proportions differ meaningfully between grade levels for lunch choices. Calculate conditional frequencies using subgroup totals: for grade 9, salad is 26/80 = 0.325; for grade 10, salad is 54/90 = 0.60. Locate cells for salad in each grade (26 and 54) and divide by grade totals (80 and 90). The computation shows grade 10 has a higher proportion choosing salad (60%) than grade 9 (32.5%), implying an association where grade level relates to preference for salad over pizza. For association, compare these conditional frequencies across groups; a difference suggests the variables are related rather than independent. A common misconception is judging association by counts alone, like more pizza overall, instead of proportions within groups. To transfer, translate comparisons by computing ratios within each row total and noting if they differ substantially.

Joint relative frequency is the proportion of the entire sample in the intersection of visited library and prefers nonfiction. The denominator is the grand total (160 students). Locate the cell for visited yes and prefer nonfiction (18 students) and the overall total (160). Compute the frequency as $18 \div 160$, which equals 0.1125 or 11.25%. A common misconception is using a marginal total like the nonfiction column (62) instead, giving $\frac{18}{62} \approx 29%$. To transfer this strategy, find the joint by dividing the intersection cell by the grand total for the overall proportion.

Association is evaluated by comparing conditional relative frequencies across groups to check if turning in on time differs by planner use. Calculate conditional frequencies using subgroup totals: for planner yes, on time is 72/90 = 0.80; for no, it's 36/90 = 0.40. Locate cells for on time in each group (72 and 36) and divide by group totals (90 each). The computation shows planner users have a higher proportion on time (80%) than non-users (40%), implying an association between planner use and timeliness. For association, compare these conditional frequencies across groups; the difference suggests the variables are connected. A common misconception is using overall counts, like more on time total, instead of within-group proportions. To transfer, compute ratios within each row and compare to identify differences in behavior by group.

Conditional relative frequency measures the proportion of one category within a specific subgroup, here the percentage of students preferring morning study given they participate in a club. The denominator is the subgroup total, which is the total for club participants (80 students). Locate the cell for club yes and prefer morning (28 students) and the subgroup total (80). Compute the frequency as 28 divided by 80, which equals 0.35 or 35%. A common misconception is using the overall total (150) instead of the subgroup, which would incorrectly give 28/150 ≈ 18.7%. To transfer this strategy, interpret 'given that the student participates in an after-school club' as using the club yes total (80) as the denominator, then divide the relevant cell (28) by it to find the ratio.

This question seeks the joint relative frequency of being in an honors class and preferring science, as a proportion of the total sample. The denominator is the grand total of 90 students. Find the intersecting cell for honors and science preference, which is 24, and divide by 90 to get approximately 0.267. A common misconception is using a subgroup total like the honors row of 30, giving 24/30 = 0.8, which is conditional instead. To transfer this strategy, pinpoint the joint cell and divide by the entire table total to obtain the joint frequency.