Question
A survey of a company's employees explored the relationship between employee status and support of a new workplace safety policy. The results are displayed in the following two-way frequency table.
Workplace Safety Policy
For Against Total
Part-Time Employee 20 60 80
Full-Time Employee 100 20 120
Total 120 80 200
Based on the table above, which of the following statements are true?
There are twice as many part-time employees against the workplace safety policy than full-time employees against the workplace safety policy.
There are more employees for the workplace safety policy than against the workplace safety policy.
There is an equal number of part-time employees and full-time employees.
There are more part-time employees against the workplace safety policy than for the workplace safety policy.
A.
II and IV
B.
I and IV
C.
II and III
D.
I and II
Workplace Safety Policy
For Against Total
Part-Time Employee 20 60 80
Full-Time Employee 100 20 120
Total 120 80 200
Based on the table above, which of the following statements are true?
There are twice as many part-time employees against the workplace safety policy than full-time employees against the workplace safety policy.
There are more employees for the workplace safety policy than against the workplace safety policy.
There is an equal number of part-time employees and full-time employees.
There are more part-time employees against the workplace safety policy than for the workplace safety policy.
A.
II and IV
B.
I and IV
C.
II and III
D.
I and II
Answers
GPT-4o mini
To analyze the statements based on the provided two-way frequency table, let's summarize the data first:
1. **Part-Time Employees**
- For the policy: 20
- Against the policy: 60
- Total: 80
2. **Full-Time Employees**
- For the policy: 100
- Against the policy: 20
- Total: 120
3. **Total**
- For the policy: 120 (20 + 100)
- Against the policy: 80 (60 + 20)
- Grand Total: 200
Now let's evaluate the statements one by one:
**I. There are twice as many part-time employees against the workplace safety policy than full-time employees against the workplace safety policy.**
- Part-time employees against: 60
- Full-time employees against: 20
- 60 is indeed three times 20, so this statement is **False**.
**II. There are more employees for the workplace safety policy than against the workplace safety policy.**
- Employees for the policy: 120
- Employees against the policy: 80
- 120 > 80, so this statement is **True**.
**III. There is an equal number of part-time employees and full-time employees.**
- Part-time employees: 80
- Full-time employees: 120
- 80 ≠ 120, so this statement is **False**.
**IV. There are more part-time employees against the workplace safety policy than for the workplace safety policy.**
- Part-time employees against: 60
- Part-time employees for: 20
- 60 > 20, so this statement is **True**.
Based on the evaluation:
- True statements: II and IV
- False statements: I and III
The correct answer is **A. II and IV**.
1. **Part-Time Employees**
- For the policy: 20
- Against the policy: 60
- Total: 80
2. **Full-Time Employees**
- For the policy: 100
- Against the policy: 20
- Total: 120
3. **Total**
- For the policy: 120 (20 + 100)
- Against the policy: 80 (60 + 20)
- Grand Total: 200
Now let's evaluate the statements one by one:
**I. There are twice as many part-time employees against the workplace safety policy than full-time employees against the workplace safety policy.**
- Part-time employees against: 60
- Full-time employees against: 20
- 60 is indeed three times 20, so this statement is **False**.
**II. There are more employees for the workplace safety policy than against the workplace safety policy.**
- Employees for the policy: 120
- Employees against the policy: 80
- 120 > 80, so this statement is **True**.
**III. There is an equal number of part-time employees and full-time employees.**
- Part-time employees: 80
- Full-time employees: 120
- 80 ≠ 120, so this statement is **False**.
**IV. There are more part-time employees against the workplace safety policy than for the workplace safety policy.**
- Part-time employees against: 60
- Part-time employees for: 20
- 60 > 20, so this statement is **True**.
Based on the evaluation:
- True statements: II and IV
- False statements: I and III
The correct answer is **A. II and IV**.