First "Tools" World Activity: Building a Model

First "Tools" World Activity: Building a Model

Samples tell stories: What can we learn from samples?

Introduction

In the last Activity we explored research questions about the Radon gas in the real world. We ended our last meeting referring to the uncertainty about our ability to formulate inferences about the year-long behavior of the Radon gas, from a sample of 72 cases (3 full days), that we collected with a long-term measurement device in the scientists’ lab.

We shall now transition to the "tools" world (the probability world) and try to examine, with a population that we generate can you even learn about the Radon’s year-long behavior, based on a sample of 72 cases?

With the "data generating machine" (called Sampler) in the TinkerPlots software, we shall describe the year-long behavior of the Radon gas (the population), in relation to the research questions we explored in the real-world, as we conjecture it to be.

Remember: this is not really the population, just what we conjecture about it.

Guidelines

1. Press on the "Tinker" icon on your computer’s desktop.

2. Save the file on your computer’s desktop.

3. Work according to the guidelines bellow.

4. Upon completion, save the file in the suitable folder.

Remember to save your work every few minutes!

Planning the "machine"

1. What is the research question you posed about the sample of 72 cases and what are the inferences you formulated from the data?

Question: ______________________________________________________

Inferences: _____________________________________________________

2. In a new TinkerPlots file: Drag the "data building machine" (Sampler) from the top menu. Change the number of sampled properties from Draw 2 to Draw 1.

With the machine, describe how the year-long behavior looks like, in your opinion, in relation to the research question that you explored (use one of the tools from the bottom ruler of the machine to create the description of each of the properties that relates to your research question)

3. Explain in your own words what does the machine describe?

4. Does the machine you built represent the population? Explain:

Second "tools" world activity: Generating samples and comparing between samples

Part 1: First sample

Now with the help of the "Sampler", generate a random sample of 72 cases from the machine that you built (press "RUN") and add a graph of the sample you got

1. Analyze the data of the first sample you got with the purpose of examining what inferences you can formulate about the research question you posed

2. What characterizes the sample you generated?

3. To what extent do the results in the sample you generated represent the Radon’s year-long behavior? Explain.

Part 2: generating multiple samples and comparing them

Generate from the machine another sample size 72

4. What characterizes the sample you generated?

In what ways is it similar to the previous sample you generated?

In what ways is it different from the previous sample you generated?

5. To what extent do the results in the sample represent the behavior of the population you built in the machine? Explain.

6. If you will generate another sample, what will it, in your opinion, show? To what extent will its results be similar to the population you built in the machine?

7. Generate several additional samples size 72, compare them to the previous samples. Describe how you compared between them?

8. What did you learn from generating the samples about the behavior of random samples size 72?

9. During the process of generating the samples, did you encounter any surprising or unexpected results? What were they and why were they surprising?

10. To what extent do you believe that we can learn from samples size 72, that were sampled from the population you built in the machine? Explain.

11.Can we learn about our research question about the Radon’s year-long behavior, with a sample of 72 cases? Explain.