a survey of 36 randomly selected students who dropped a course was conducted at a college. the following results were collected. complete parts (a) through (c).
full data set
f personal m course m course
m work f personal m course
f work m work m personal
m personal f course f course
m course f personal m course
m personal f personal m course
m course f work m course
f personal f course f work
f personal f course m work
f personal f work m course
f work m work f personal
f personal f personal m work

(a) construct a contingency table for the two variables.
course personal work
male
female

Question

a survey of 36 randomly selected students who dropped a course was conducted at a college. the following results were collected. complete parts (a) through (c).
full data set
f personal m course m course
m work f personal m course
f work m work m personal
m personal f course f course
m course f personal m course
m personal f personal m course
m course f work m course
f personal f course f work
f personal f course m work
f personal f work m course
f work m work f personal
f personal f personal m work

(a) construct a contingency table for the two variables.
course personal work
male
female

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Contingency Table", "Two-Way Frequency Table" ], "current_concepts": [ "Contingency Table", "Two-Way Frequency Table", "Categorical Data Analysis" ] } ## Identify the categories and variables We have two categorical variables: 1. Gender: Male (M) and Female (F). 2. Reason for dropping: Course, Personal, and Work. ## Count the occurrences for Male (M) Let's count each reason for students labeled "M": - Row 1: `M Course`, `M Course` (2 Course) - Row 2: `M Work`, `M Course` (1 Work, 1 Course) - Row 3: `M Work`, `M Personal` (1 Work, 1 Personal) - Row 4: `M Personal` (1 Personal) - Row 5: `M Course`, `M Course` (2 Course) - Row 6: `M Personal`, `M Course` (1 Personal, 1 Course) - Row 7: `M Course`, `M Course` (2 Course) - Row 8: None - Row 9: `M Work` (1 Work) - Row 10: `M Course` (1 Course) - Row 11: `M Work` (1 Work) - Row 12: `M Work` (1 Work) Let's sum the counts for Male (M): - **Course**: 2 (Row 1) + 1 (Row 2) + 2 (Row 5) + 1 (Row 6) + 2 (Row 7) + 1 (Row 10) = 9 - **Personal**: 1 (Row 3) + 1 (Row 4) + 1 (Row 6) = 3 - **Work**: 1 (Row 2) + 1 (Row 3) + 1 (Row 9) + 1 (Row 11) + 1 (Row 12) = 5 Total Male = $9 + 3 + 5 = 17$. ## Count the occurrences for Female (F) Let's count each reason for students labeled "F": - Row 1: `F Personal` (1 Personal) - Row 2: `F Personal` (1 Personal) - Row 3: `F Work` (1 Work) - Row 4: `F Course`, `F Course` (2 Course) - Row 5: `F Personal` (1 Personal) - Row 6: `F Personal` (1 Personal) - Row 7: `F Work` (1 Work) - Row 8: `F Personal`, `F Course`, `F Work` (1 Personal, 1 Course, 1 Work) - Row 9: `F Personal`, `F Course` (1 Personal, 1 Course) - Row 10: `F Personal`, `F Work` (1 Personal, 1 Work) - Row 11: `F Work`, `F Personal` (1 Work, 1 Personal) - Row 12: `F Personal`, `F Personal` (2 Personal) Let's sum the counts for Female (F): - **Course**: 2 (Row 4) + 1 (Row 8) + 1 (Row 9) = 4 - **Personal**: 1 (Row 1) + 1 (Row 2) + 1 (Row 5) + 1 (Row 6) + 1 (Row 8) + 1 (Row 9) + 1 (Row 10) + 1 (Row 11) + 2 (Row 12) = 11 - **Work**: 1 (Row 3) + 1 (Row 7) + 1 (Row 8) + 1 (Row 10) + 1 (Row 11) = 5 Total Female = $4 + 11 + 5 = 20$. Let's double check the total count: Total observations = $17 \text{ (Male)} + 20 \text{ (Female)} = 37$. Wait, let's recount the total rows and entries in the table. The table has 12 rows and 3 columns = 36 entries. Let's re-verify each entry carefully: Row-by-row verification: 1. `F Personal` | `M Course` | `M Course` -> F: 1 Personal; M: 2 Course 2. `M Work` | `F Personal` | `M Course` -> F: 1 Personal; M: 1 Work, 1 Course 3. `F Work` | `M Work` | `M Personal` -> F: 1 Work; M: 1 Work, 1 Personal 4. `M Personal` | `F Course` | `F Course` -> F: 2 Course; M: 1 Personal 5. `M Course` | `F Personal` | `M Course` -> F: 1 Personal; M: 2 Course 6. `M Personal` | `F Personal` | `M Course` -> F: 1 Personal; M: 1 Personal, 1 Course 7. `M Course` | `F Work` | `M Course` -> F: 1 Work; M: 2 Course 8. `F Personal` | `F Course` | `F Work` -> F: 1 Personal, 1 Course, 1 Work 9. `F Personal` | `F Course` | `M Work` -> F: 1 Personal, 1 Course; M: 1 Work 10. `F Personal` | `F Work` | `M Course` -> F: 1 Personal, 1 Work; M: 1 Course 11. `F Work` | `M Work` | `F Personal` -> F: 1 Work, 1 Personal; M: 1 Work 12. `F Personal` | `F Personal` | `M Work` -> F: 2 Personal; M: 1 Work Let's sum again: **Male (M):** - Course: Row 1 (2), Row 2 (1), Row 5 (2), Row 6 (1), Row 7 (2), Row 10 (1) -> Total = $2+1+2+1+2+1 = 9$ - Personal: Row 3 (1), Row 4 (1), Row 6 (1) -> Total = $1+1+1 = 3$ - Work: Row 2 (1), Row 3 (1), Row 9 (1), Row 11 (1), Row 12 (1) -> Total = $1+1+1+1+1 = 5$ Total Male = $9 + 3 + 5 = 17$. **Female (F):** - Course: Row 4 (2), Row 8 (1), Row 9 (1) -> Total = $2+1+1 = 4$ - Personal: Row 1 (1), Row 2 (1), Row 5 (1), Row 6 (1), Row 8 (1), Row 9 (1), Row 10 (1), Row 11 (1), Row 12 (2) -> Total = $1+1+1+1+1+1+1+1+2 = 10$ - Work: Row 3 (1), Row 7 (1), Row 8 (1), Row 10 (1), Row 11 (1) -> Total = $1+1+1+1+1 = 5$ Total Female = $4 + 10 + 5 = 19$. Grand Total = $17 + 19 = 36$. This matches the 36 students surveyed. ## Construct the contingency table The table structure is: - Rows: Male, Female - Columns: Course, Personal, Work - Male: Course = 9, Personal = 3, Work = 5 - Female: Course = 4, Personal = 10, Work = 5 | | Course | Personal | Work | |---|---|---|---| | **Male** | 9 | 3 | 5 | | **Female** | 4 | 10 | 5 | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Contingency Table" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the categories and variables

Count the occurrences for Male (M)

Count the occurrences for Female (F)

Answer: