QuestionAugust 25, 2025

11. Organize the results in a two-way table.Include the marginal frequencies. You conduct a survey that asks 32 students in your class whether they have pets or siblings. The results show that 21 of the students surveyed have siblings, 13 have pets, and 4 have no siblings or pets.

11. Organize the results in a two-way table.Include the marginal frequencies. You conduct a survey that asks 32 students in your class whether they have pets or siblings. The results show that 21 of the students surveyed have siblings, 13 have pets, and 4 have no siblings or pets.
11. Organize the results in a two-way table.Include the marginal frequencies. You conduct a survey that asks 32 students in your class whether they have pets or siblings. The results show that 21 of the students surveyed have siblings, 13 have pets, and 4 have no siblings or pets.

Solution
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Answer

\[ \begin{array}{c|c|c|c} & \text{Pets} & \text{No Pets} & \text{Total} \\ \hline \text{Siblings} & 6 & 15 & 21 \\ \text{No Siblings} & 7 & 4 & 11 \\ \hline \text{Total} & 13 & 19 & 32 \\ \end{array} \] Explanation 1. Determine Total Students with Siblings or Pets Subtract students with neither from total: 32 - 4 = 28. 2. Calculate Students with Only Siblings Subtract students with neither and those with pets from siblings: 21 - (28 - 21) = 11. 3. Calculate Students with Only Pets Subtract students with neither and those with siblings from pets: 13 - (28 - 13) = 5. 4. Calculate Students with Both Siblings and Pets Use the formula for intersection: |S \cap P| = |S| + |P| - |S \cup P| = 21 + 13 - 28 = 6. 5. Construct Two-Way Table Organize data into a table format including marginal frequencies.

Explanation

1. Determine Total Students with Siblings or Pets<br /> Subtract students with neither from total: $32 - 4 = 28$.<br /><br />2. Calculate Students with Only Siblings<br /> Subtract students with neither and those with pets from siblings: $21 - (28 - 21) = 11$.<br /><br />3. Calculate Students with Only Pets<br /> Subtract students with neither and those with siblings from pets: $13 - (28 - 13) = 5$.<br /><br />4. Calculate Students with Both Siblings and Pets<br /> Use the formula for intersection: $|S \cap P| = |S| + |P| - |S \cup P| = 21 + 13 - 28 = 6$.<br /><br />5. Construct Two-Way Table<br /> Organize data into a table format including marginal frequencies.
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