Homer Simpson tests if salt intake affects heart rate, while Mr. Burns tests if free lunch improves worker productivity, both with labeled experimental components.

Problem Analysis:

The task involves identifying key components of experimental designs and drawing conclusions based on the results. Let's break it down into two scenarios:

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Scenario 1: Mr. Nick Advises Homer

#### Task:
Mr. Nick advises Homer to reduce his salt intake because he believes it will lower Homer's heart rate. To test this idea, Homer eats all the salty food he loves for a week and measures his heart rate daily. His average heart rate is 113 bpm (beats per minute). In his next experiment, he spends a week not eating any salty food. This week, his average heart rate was 95 bpm.

#### Questions:
1. Control: What remains constant or unchanged in the experiment?
2. Manipulated (Independent) Variable: What is being changed or manipulated by Homer?
3. Responding (Dependent) Variable: What is being measured as a result of the change?
4. Conclusion: Based on the results, what should Homer conclude?

#### Solution:
1. Control: The control in this experiment is Homer himself, including his overall health, lifestyle, and other factors that remain constant throughout the experiment.
2. Manipulated (Independent) Variable: The amount of salt in Homer's diet is the manipulated variable. He changes his salt intake from high (eating salty food) to low (not eating salty food).
3. Responding (Dependent) Variable: The responding variable is Homer's heart rate, which is measured daily and averages to 113 bpm with salty food and 95 bpm without salty food.
4. Conclusion: Based on the results, Homer should conclude that reducing his salt intake lowers his heart rate. The decrease in heart rate from 113 bpm to 95 bpm suggests that salt consumption has a direct impact on his heart rate.

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Scenario 2: Mr. Burns' Experiment

#### Task:
Mr. Burns believes giving his workers free lunch will improve productivity at the plant. To test this idea, he gives half of the workers free lunch (pizza every day for a month), while the other group must bring their own lunch. At the end of the month, he measures productivity by examining the number of completed jobs. The group that received free lunch completed more jobs than the group that didn't.

#### Questions:
5. Control: What remains constant or unchanged in the experiment?
6. Manipulated (Independent) Variable: What is being changed or manipulated by Mr. Burns?
7. Responding (Dependent) Variable: What is being measured as a result of the change?
8. Conclusion: Based on the results, what should Mr. Burns conclude?

#### Solution:
5. Control: The control in this experiment includes the workers' baseline productivity, the nature of the work they perform, and other environmental factors that remain constant.
6. Manipulated (Independent) Variable: The manipulated variable is whether the workers receive free lunch (pizza) or must bring their own lunch.
7. Responding (Dependent) Variable: The responding variable is the productivity of the workers, measured by the number of completed jobs.
8. Conclusion: Based on the results, Mr. Burns should conclude that providing free lunch improves worker productivity. The group that received free lunch completed more jobs than the group that did not, suggesting a positive correlation between free lunch and productivity.

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Final Answers:

1. Control: Homer himself (his overall health, lifestyle, etc.)
2. Manipulated (Independent) Variable: Amount of salt in Homer's diet
3. Responding (Dependent) Variable: Homer's heart rate
4. Conclusion: Reducing salt intake lowers heart rate.
5. Control: Workers' baseline productivity and environmental factors
6. Manipulated (Independent) Variable: Whether workers receive free lunch
7. Responding (Dependent) Variable: Number of completed jobs (productivity)
8. Conclusion: Providing free lunch improves worker productivity.

Boxed Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \text{Homer himself (his overall health, lifestyle, etc.)} \\
2. & \text{Amount of salt in Homer's diet} \\
3. & \text{Homer's heart rate} \\
4. & \text{Reducing salt intake lowers heart rate.} \\
5. & \text{Workers' baseline productivity and environmental factors} \\
6. & \text{Whether workers receive free lunch} \\
7. & \text{Number of completed jobs (productivity)} \\
8. & \text{Providing free lunch improves worker productivity.}
\end{array}
}
\]