Diagrams showing how to identify control groups and variables in experiments, using examples with Homer Simpson and Mr. Burns.

Let's solve each part of the problem step by step, identifying the controls, independent (manipulated) variables, dependent (responding) variables, and drawing appropriate conclusions for both scenarios.

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Scenario 1: Dr. Nick advises Homer to reduce salt intake

Situation:
Homer eats a low-salt diet for a week and records his average heart rate as 115 bpm. In the next week, he eats no salty food at all, and his heart rate drops to 95 bpm.

#### 1. Control
- The control is the condition that remains unchanged or serves as a baseline for comparison.
- Here, the first week (low-salt diet) is the control because it’s the initial condition before the change.
- Answer: *The first week when Homer ate a low-salt diet (heart rate = 115 bpm).*

#### 2. Manipulated (Independent) Variable
- This is what the experimenter changes intentionally.
- Dr. Nick advised Homer to stop eating any salty food in the second week.
- So, the amount of salt in the diet is changed.
- Answer: *Amount of salt in Homer’s diet.*

#### 3. Responding (Dependent) Variable
- This is what is measured or observed in response to the change.
- Homer’s average heart rate is recorded.
- Answer: *Average heart rate (beats per minute).*

#### 4. What should his conclusion be?
- From the data:
- Week 1 (low salt): 115 bpm
- Week 2 (no salt): 95 bpm
- Heart rate decreased after eliminating salt.
- Conclusion: *Reducing salt intake may lower heart rate.*
- However, this is only one person and two weeks — not a controlled experiment with multiple subjects.
- Answer: *Eliminating salty foods appears to lower Homer’s heart rate, suggesting that salt intake may affect heart rate.*

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Scenario 2: Mr. Burns gives free lunch to workers

Situation:
Mr. Burns believes giving free lunch will improve productivity. Half the workers get free lunch every day; the other half must bring their own. At the end of the month, productivity is measured by number of completed jobs. The group with free lunch completed more jobs.

#### 5. Control
- The group that does not receive free lunch (must bring their own) is the control group.
- Answer: *The group of workers who did not receive free lunch (had to bring their own).*

#### 6. Manipulated (Independent) Variable
- The factor being changed is whether or not workers receive free lunch.
- Answer: *Whether workers received free lunch or not.*

#### 7. Responding (Dependent) Variable
- The outcome being measured is productivity, specifically the number of completed jobs.
- Answer: *Number of completed jobs (productivity).*

#### 8. What should his conclusion be?
- The group with free lunch had higher productivity.
- But we must consider other factors (e.g., motivation, morale, time saved).
- Based on the data provided:
- Conclusion: *Providing free lunch may increase worker productivity, as the group receiving free lunch completed more jobs.*
- However, this is observational and may have confounding variables.
- Answer: *Giving free lunch may lead to increased productivity, based on the results of this experiment.*

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✔ Final Answers:

#### Scenario 1: Homer and Salt Intake
1. Control: The first week when Homer ate a low-salt diet (heart rate = 115 bpm)
2. Manipulated (Independent) Variable: Amount of salt in Homer’s diet
3. Responding (Dependent) Variable: Average heart rate (beats per minute)
4. Conclusion: Eliminating salty foods appears to lower Homer’s heart rate, suggesting salt intake may affect heart rate.

#### Scenario 2: Mr. Burns and Free Lunch
5. Control: The group of workers who did not receive free lunch (had to bring their own)
6. Manipulated (Independent) Variable: Whether workers received free lunch or not
7. Responding (Dependent) Variable: Number of completed jobs (productivity)
8. Conclusion: Providing free lunch may increase worker productivity, as the group receiving free lunch completed more jobs.

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Let me know if you'd like a diagram or visual representation!