Worksheet on identifying independent and dependent variables in science experiments.

Problem Analysis:

The image contains two separate experiments described in a worksheet. Let's break them down and solve each one step by step.

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#### Experiment 1: Simpson's Special Juice
Scenario:
Simpsons thinks that a special juice will increase the productivity of workers. He creates two groups of 50 workers each and assigns each group the same task (in this case, they are supposed to staple sets of papers). Group 1 drinks 100ml of the special juice while Group 2 drinks 50ml of the special juice. After an hour, Simpsons counts how many sets of papers each group stapled. The data is provided in the table below:

| Group | Number of sets of papers stapled |
|-------|-----------------------------------|
| Group 1 | 1,110 |
| Group 2 | 1,130 |

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##### Solution Steps:

1. Identify the Variables:
- Independent Variable: The amount of special juice consumed by the workers. This is what Simpson manipulated between the two groups.
- Dependent Variable: The number of sets of papers stapled by the workers. This is the outcome measured to determine the effect of the independent variable.
- Controlled Variable: Factors that remain constant across both groups to ensure a fair comparison. These could include:
- The task assigned (stapling sets of papers).
- The time given for the task (1 hour).
- The number of workers in each group (50 workers per group).
- The environment where the task is performed (e.g., lighting, noise level).

2. What Should Simpson's Conclusion Be?
- From the data:
- Group 1 (100ml of juice) stapled 1,110 sets.
- Group 2 (50ml of juice) stapled 1,130 sets.
- Group 2, which drank less juice, actually stapled more sets of papers than Group 1. This suggests that drinking more of the special juice did not increase productivity; in fact, it might have had the opposite effect.
- Conclusion: Simpson should conclude that drinking more of the special juice does not increase productivity and may even decrease it based on the observed data.

3. How Did Simpson Determine How Many Sets of Papers Each Group Stapled?
- Simpson likely counted the total number of sets of papers stapled by all workers in each group after the 1-hour task period. Since there were 50 workers in each group, he could calculate the average productivity per worker if needed.

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#### Experiment 2: Homer's Coconut Juice Observation
Scenario:
Homer notices that his doctor is covered in a strange green rash. His friend Barney tells him that coconut juice cures most things. Homer decides to check this out by exposing two sections of his skin to the rash and then applying coconut juice to one section as a "treatment." After 48 hours, there is no change in the appearance of the green stuff on either part of his body.

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##### Solution Steps:

1. Identify the Variables:
- Independent Variable: Whether or not the coconut juice was applied to the skin. This is the factor being manipulated (one section with coconut juice, one without).
- Dependent Variable: The appearance of the green rash on Homer's skin. This is the outcome being observed to determine the effect of the independent variable.
- Controlled Variable: Factors that remain constant to ensure a fair comparison. These could include:
- The duration of exposure to the rash (48 hours).
- The size and location of the skin sections exposed to the rash.
- The condition of Homer's skin before the experiment.

2. What Is a Hypothesis Homer Could Write About His Observation?
- A hypothesis is a testable statement predicting the relationship between variables. Based on Barney's claim, Homer might hypothesize:
- Hypothesis: Applying coconut juice to the rash will reduce or eliminate the green rash within 48 hours.

3. Was There Any Change in the Appearance of the Green Stuff on Either Part of His Body?
- No, there was no change in the appearance of the green rash on either part of Homer's body after 48 hours. Both sections looked the same.

4. If Not, Why Not?
- Possible reasons why there was no change:
- The coconut juice might not have any curative properties for the green rash.
- The duration of the experiment (48 hours) might not have been long enough to observe any effects.
- The green rash might be caused by something unrelated to what coconut juice can treat.
- Homer's skin might not have absorbed the coconut juice effectively.

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#### Experiment 3: Krusty's New Iching Powder
Scenario:
Krusty was testing a new itching powder. He wanted to see if it was stronger than his original itching powder. He bought 10 volunteers and split them into two groups. Interested in this product, he buys 10 subjects and splits them up into two groups. One group gets the new itching powder, and the other gets the original itching powder. His results are below:

| Subject | Time Until Itching Began (minutes) |
|---------|-------------------------------------|
| Subject A | 30 minutes |
| Subject B | 45 minutes |

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##### Solution Steps:

1. Identify the Variables:
- Independent Variable: The type of itching powder used (new itching powder vs. original itching powder). This is what Krusty manipulated between the two groups.
- Dependent Variable: The time until itching began for each subject. This is the outcome measured to determine the effect of the independent variable.

2. What Should Krusty's Conclusion Be?
- From the data:
- Subject A (new itching powder) started itching after 30 minutes.
- Subject B (original itching powder) started itching after 45 minutes.
- The new itching powder caused itching to begin sooner than the original itching powder. This suggests that the new itching powder might be stronger.
- Conclusion: Krusty should conclude that the new itching powder appears to be stronger than the original itching powder based on the observed data.

3. How Could Krusty Improve His Experiment?
- Krusty's experiment has only two subjects, which is a very small sample size. To improve the reliability and validity of his results, he should:
- Increase the number of subjects in each group to gather more data points.
- Randomly assign subjects to the two groups to minimize bias.
- Ensure that all other conditions (e.g., environment, instructions) are controlled so that the only variable affecting the results is the type of itching powder.
- Use statistical methods to analyze the data if the sample size is large enough.

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Final Answers:

1. Simpsons' Experiment:
- Independent Variable: Amount of special juice consumed.
- Dependent Variable: Number of sets of papers stapled.
- Controlled Variables: Task, time, number of workers, environment.
- Conclusion: Drinking more of the special juice does not increase productivity and may decrease it.

2. Homer's Experiment:
- Independent Variable: Application of coconut juice.
- Dependent Variable: Appearance of the green rash.
- Controlled Variables: Duration of exposure, skin sections, initial skin condition.
- Hypothesis: Coconut juice will reduce or eliminate the green rash.
- No change in the rash; possible reasons include ineffectiveness of coconut juice or insufficient duration.

3. Krusty's Experiment:
- Independent Variable: Type of itching powder.
- Dependent Variable: Time until itching began.
- Conclusion: The new itching powder appears to be stronger.
- Improvement: Increase sample size, randomize subjects, control conditions, use statistics.

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Final Answer Box:
\boxed{
\text{See detailed solutions above.}
}