91影视

According to the popular TV show Mythbusters, the answer is 鈥淵es.鈥� In the March 9, 2005, episode, the Mythbusters team presented the results of an experiment involving 50 subjects. All the subjects were placed in a booth for an extended period of time and monitored by hidden camera. Two-thirds of the subjects were given a 鈥測awn seed鈥� by one of the experimenters; that is, the experimenter yawned in the subject鈥檚 presence prior to leaving the room. The remaining subjects were given no yawn seed. What were the results? Of the 16 subjects who had no yawn seed, 4 yawned. Of the 34 subjects given a yawn seed, 10 yawned. Adam Savage and Jamie Hyneman, the cohosts of Mythbusters, used these results to conclude that yawning is contagious. (a) Explain how you could use slips of paper to randomly reassign the subjects to the treatment groups. (b) Suppose we used your method in (a) to redo the random assignment 50 times. The Fathom dot plot displays the number of subjects in the yawn seed group who yawned in each of these random assignments. What conclusion would you draw about whether yawning is contagious? Explain.

Step by step solution

01

Understanding the Problem

First, we need to understand the problem setup: there are 50 subjects, divided into two groups. The first group consists of 34 subjects given a 'yawn seed', and the second group consists of 16 subjects without a 'yawn seed'. We are tasked with examining whether yawning is contagious based on the experiment's outcome.

02

Developing the Random Assignment Method

To randomly reassign subjects to new groups using slips of paper, write 'Yawn Seed' on 34 slips and 'No Yawn Seed' on 16 slips. Each subject would then draw one slip to determine their assignment to a group, simulating random assignment for the experiment.

03

Evaluating the Hypothesis Using Random Assignment

Simulate the experiment multiple times (e.g., 50 times) using the random assignment method from Step 2. In each simulation, count how many subjects yawn in the 'Yawn Seed' group and record these numbers. This data can show the expected yawning distribution purely by chance.

04

Analyzing the Dot Plot

Analyze the dot plot that shows the number of subjects yawning in the 'Yawn Seed' group across the 50 random assignments. Observe where the original 10 yawning subjects fall within the distribution.

05

Drawing a Conclusion

Compare the original result (10 subjects yawning in the yawn seed group) to the results of your random assignments. If the number 10 lies far outside the typical range observed in random assignments, it suggests yawning is contagious as it happens more often than expected by chance.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Experimental Design

In any scientific inquiry, having a solid experimental design is crucial. It ensures that the results are reliable and that the experiment addresses the research question effectively. In the Mythbusters episode, the experiment aimed to test whether yawning is contagious by observing the participants' reactions. The design involved a controlled setting where participants were exposed to a 'yawn seed'.
The key components of an effective experimental design include:

• Clearly defining the research question.
• Identifying variables 鈥� in this case, the presence or absence of the 'yawn seed'.
• Ensuring that external factors are minimized to prevent them from influencing the outcomes.

By carefully structuring the experiment, researchers can gather data that more accurately reflects the relationship between the variables involved. In this context, having the control group (no yawn seed) and the treatment group (yawn seed) helps in showcasing any difference in yawning patterns between the two conditions.

Random Assignment

Random assignment is a method used to ensure that each participant has an equal chance of being placed in any group. This is key to avoiding bias and making sure the results are due to the treatment rather than other variables. In the Mythbusters exercise, using slips of paper to assign participants to groups randomly provides a simple yet effective approach.
Here鈥檚 how it works:

• Have 34 slips marked 'Yawn Seed' and 16 marked 'No Yawn Seed'.
• Participants draw slips to ascertain their assignment, ensuring a random distribution between groups.

By assigning subjects randomly, any differences in yawning can be more confidently attributed to the 'yawn seed' rather than preexisting participant characteristics. This practice is essential for a fair test, ensuring equal initial conditions for each group.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. In our scenario, the hypothesis is whether yawning is indeed contagious according to the experiment's setup and results. The null hypothesis would assert that the 'yawn seed' has no effect on the likelihood of yawning.
The process of hypothesis testing generally involves:

• Formulating the null and alternative hypotheses.
• Collecting and analyzing sample data.
• Determining the p-value to assess the likelihood of observing the data under the null hypothesis.
• Making a decision to either reject or not reject the null hypothesis based on a predetermined significance level, often 0.05.

In the Mythbusters experiment, analyzing whether the original outcome of 10 yawns in the 'yawn seed' group falls far outside the range expected by chance helps in deciding if the null hypothesis can be rejected. This suggests that yawning might indeed be contagious.

Statistical Analysis

Statistical analysis involves examining data sets to draw conclusions. It's particularly useful in understanding experiments' outcomes and validating research. In the context of yawning and its contagiousness, statistical analysis was employed by Mythbusters to interpret whether the yawning observed was due to chance or influence of the 'yawn seed'.
The process often involves:

• Compiling data from a sample and possibly visualizing it in forms like dot plots.
• Computing statistical measures to describe and understand the data's distribution.
• Comparing the experimental result to a typical random assignment scenario to see how it fits into expected patterns.

In the experiment, the statistical analysis might reveal that the observed frequency of yawning with the 'yawn seed' is unlikely to be due to random variation alone. Using techniques such as analyzing a dot plot helps confirm whether the results are statistically significant, thus supporting the claim of yawning's contagious nature.