Question

fiona interviewed her 30 classmates on whether or not they had a sibling and if they have assigned chores at home. she displayed her results in the two - way table shown (table with columns have a sibling, only child and rows have chores, do not have chores with values 7, 9 and 8, 6 respectively). which category had the highest marginal relative frequency? a only child b have a sibling c do not have chores d have chores

Explanation:

Step1: Recall Marginal Relative Frequency

Marginal relative frequency for a row or column is the sum of the frequencies in that row or column divided by the total number of observations (30 here).

Step2: Calculate Marginal Relative Frequency for Each Category

• For "Only Child" (column total): Sum of "Have Chores" and "Do Not Have Chores" for Only Child: \(9 + 6 = 15\). Marginal relative frequency: \(\frac{15}{30}=0.5\).
• For "Have a Sibling" (column total): \(7 + 8 = 15\). Marginal relative frequency: \(\frac{15}{30}=0.5\). Wait, no, wait. Wait, rows: "Have Chores" row total: \(7 + 9 = 16\). Marginal relative frequency: \(\frac{16}{30}\approx0.533\). "Do Not Have Chores" row total: \(8 + 6 = 14\). Marginal relative frequency: \(\frac{14}{30}\approx0.467\). Wait, columns: "Only Child" column total: \(9 + 6 = 15\) (\(\frac{15}{30}=0.5\)), "Have a Sibling" column total: \(7 + 8 = 15\) (\(\frac{15}{30}=0.5\)). Rows: "Have Chores" row total: \(7 + 9 = 16\) (\(\frac{16}{30}\approx0.533\)), "Do Not Have Chores" row total: \(8 + 6 = 14\) (\(\frac{14}{30}\approx0.467\)). Wait, the options are A. Only Child, B. Have a Sibling, C. Do Not Have Chores, D. Have Chores. Wait, "Have Chores" row total is 16, "Only Child" column total is 15, "Have a Sibling" column total is 15, "Do Not Have Chores" row total is 14. So 16/30 is higher than 15/30 and 14/30. So "Have Chores" has higher marginal relative frequency. Wait, but let's recalculate:

Wait, total number of students is 30 (7+9+8+6=30).

Marginal relative frequency for "Only Child" (column): (9 + 6)/30 = 15/30 = 0.5.

Marginal relative frequency for "Have a Sibling" (column): (7 + 8)/30 = 15/30 = 0.5.

Marginal relative frequency for "Have Chores" (row): (7 + 9)/30 = 16/30 ≈ 0.533.

Marginal relative frequency for "Do Not Have Chores" (row): (8 + 6)/30 = 14/30 ≈ 0.467.

So 0.533 is higher than 0.5 and 0.467. So "Have Chores" (option D) has the highest marginal relative frequency. Wait, but let's check again. Wait, maybe I made a mistake. Wait, the options: A. Only Child (15/30=0.5), B. Have a Sibling (15/30=0.5), C. Do Not Have Chores (14/30≈0.467), D. Have Chores (16/30≈0.533). So D is higher.

Answer:

D. Have Chores