Please write up solutions directly in the document. Be sure to save your document as a PDF with the file name LastName_Homework3.pdf. Provide clear and complete sentences. You may work with others in the class on this assignment, but you must turn in this assignment individually and give responses in your own words.
A 2017 study (Capraro, 2017) investigated whether subjects would make an “honest” decision under pressure. Capraro’s group hypothesized that in certain circumstances, people would be more likely to make an honest decision when being pushed to act quickly. To test this hypothesis, they created a game and recruited volunteer subjects to participate.
In this game, each participant was told that they belonged to either group 1 or group 2. They were then paired with another participant and were asked which group they belonged to, and the subject could choose to either lie or tell the truth about the group they belonged to. If the subject told the truth, they and their partner received a monetary award. If the subject lied, they would receive an even larger monetary reward, and their partner would receive a smaller one. To ensure that participants understood the rules of this game, they were given comprehension questions which they needed to answer correctly to participate, resulting in the group sizes being somewhat unequal with some participants not. However, subjects were randomly assigned to either make their decision under time pressure (within 5 seconds), while others were given ample time (30 seconds) to come to a decision. The results of this study are given in the table below:
|
|
Truth
|
Lie
|
Total
|
|
5 seconds (Time Pressure)
|
85
|
65
|
150
|
|
30 seconds (Time Delay)
|
69
|
87
|
156
|
|
Total
|
154
|
152
|
306
|
Research question: Are subjects more likely to be honest when forced to answer quickly (time pressure) than they would be if given more time (time delay)?
PART 1: EXPLORING the DATA
1. Based on the table above, what was the observed difference in percentages of subjects that made the honest choice between the time pressure and time delay groups?
2. How did the researchers use randomness in their study design? What implications does this have about the conclusions the researchers can draw?
PART 2: SETTING UP A SAMPLER
3. State the null hypothesis and the alternative hypothesis for this problem.
4. Set up a model in TinkerPlots that can be used to simulate this study under the assumption of your null hypothesis. As part of your work, be sure to:
a. Copy and paste a picture of your TinkerPlots sampler below.
b. Describe the assumptions you are making, how they connect to the model you created, and how they will help you answer the research question. In your answer, be sure to connect to how your model reflects the study design you noted in question 2.
c. State what the repeat and draw values are set to and explain why they are set to those values.
d. Describe if the device(s) in your sampler are set to sample with or without replacement and explain why.
e. Describe what will happen when you click run and how this relates to the problem context.
5. Use TinkerPlots to carry out a single trial of the random assignment. Create a plot of your results in the form. of a 2x2 table, making sure to put the time pressure grouping on the y-axis, and the honesty outcome (truth/lie) on the x-axis. (Do not plot the join column.) Paste this plot below and provide an interpretation of a dot in your plot.
6. What statistic are you interested in collecting on? Explain how this statistic will help you determine if time pressure makes subjects more honest than subjects who were not subjected to the time pressure. How does the unequal group size in this study (150 vs 156) impact this choice?
7. Carry out 500 trials of the simulation in TinkerPlots. For each trial (i.e., random assignment) collect the difference in percentages between the two groups. Paste a plot of the resulting sampling distribution below and interpret what a dot represents in that plot.
PART 3: EVALUATING THE RESULTS
8. Report the p-value and interpret what this percentage means in the context of this problem. (There is an __% chance that…) Re-paste your sampling distribution to show where your p-value came from.
9. Based on your p-value, how strong is the evidence against the null model? What does this suggest about the answer to the research question?
10. Can we generalize these results to a larger population? Is there a cause-and-effect relationship that we can reveal from this study? Explain your reasoning.
SPEED SKATING
Athletes from the Netherlands have fared rather well in speed skating events. In fact, Dutch competitors in the Winter Olympics have won 130 medals, 121 in speed skating events. But are the Dutch speed skaters better or worse than those from the United States? Using data from the SpeedskatingResults.com database, random samples of 15 skaters were taken from each of the two countries’ top 100 performances in the Ladies 3000-meter event. These data can be found in the SpeedSkating.tp3 data file. You will use these data to answer the following research question:
Research question: Is there evidence that female athletes from the Netherlands have different average times in the 3000m events than female athletes from the United States?
PART 1: EXPLORING THE DATA
11. Create a plot that shows the means for each of the two countries and the difference between these two means. What is the difference in mean times between the Netherlands and the United States?
12. How did the researchers use randomness in their study design? What implications does this have about the conclusions the researchers can draw?
PART 2: SETTING UP A SAMPLER
13. State the null hypothesis and the alternative hypothesis for this problem.
14. Set up a model in TinkerPlots that can be used to simulate this study under the assumption of your null hypothesis. As part of your work, be sure to:
a. Copy and paste a picture of your TinkerPlots sampler below.
b. Describe the assumptions you are making, how they connect to the model you created, and how they will help you answer the research question. In your answer, be sure to connect to how your model reflects the study design you noted in question 2.
c. State what the repeat and draw values are set to and explain why they are set to those values.
d. Describe if the device(s) in your sampler are set to sample with or without replacement and explain why.
e. Describe what will happen when you click run and how this relates to the problem context.
15. Use TinkerPlots to carry out one randomized trial of this study. Create a plot of the results that makes it clear what the difference in means is between the two countries. Interpret what a dot in the plot represents.
16. Carry out 500 trials of the simulation in TinkerPlots, collecting on the difference in means. Paste a plot of the resulting sampling distribution below and interpret what a dot represents in that plot.
PART 3: EVALUATING THE RESULTS
17. What value is your sampling distribution centered at? Why does this make sense?
18. Report the p-value and interpret what this percentage means in the context of this problem. (There is an __% chance that…)
19. Based on your p-value, how strong is the evidence against the null model? What does this suggest about the answer to the research question?
20. Can we generalize these results to a larger population? Is there a cause-and-effect relationship that we can reveal from this study? Explain your reasoning.