Binomial models are used frequently in the social sciences. They are used to calculate the probability of events occurring. This project will focus on (1) using probability models in real-world situations and (2) binomial probability models.

To finish project, perform the following tasks:

• Design a probability model that models a real-world situation, and identify the possible outcomes and sample space of the model.
• Analyze the results of the experiment, and compare theoretical and empirical outcomes.
• Design a binomial probability experiment.

Questions:

1. Find a public opinion poll from a media source that predicts a probability. Design a probability experiment that models a political science public opinion poll.

• What are the possible outcomes and sample space of the experiment?
• What were the results of the experiment? Show the results in table format.
• What is the probability of each option?
• How can a binomial probability experiment be set up to test the accuracy of the results?

2. Compare the data from the experiment to the public opinion poll. How does the data collected compared to the media source? Describe the trends in the data and compare the theoretical probability to the empirical probability.

3. Produce a binomial probability experiment with the data from the public opinion poll experiment. Use the probability of success and failure from the experiment. Calculate the probability of the number of successes in 100 random tests. For example, if the probability of success is 0.20 and the number of trials is 100, then the number of successes is 20.

• What are the numbers of trials, successes, and failures?
• What are the results of the experiment?
• What is the difference between the empirical and theoretical probabilities? Identify trends in the outcomes.

QUESTIONS TO THE PROJECT I ALREADY ANSWERED IT!!!

Question: 1

a. For a political science public opinion poll, the possible outcomes could be the percentage of respondents who support a certain candidate or political party, and the sample space would be the entire population of eligible voters.

b. Results of the experiment:

Candidate/Party	Percentage of Support
Candidate A	40%
Candidate B	35%
Candidate C	25%

c. The probability of each option would be the percentage of support divided by 100. So, for Candidate A the probability would be 0.4, for Candidate B it would be 0.35, and for Candidate C it would be 0.25. d. A binomial probability experiment could be set up to test the accuracy of the results by randomly selecting a sample of the population and asking them which candidate they support. The number of people who support each candidate would then be recorded and compared to the results from the public opinion poll.

Question: 2

The data collected from the experiment may differ from the media source's predictions due to sampling error or other factors. It is important to note trends in the data and compare the theoretical probability (the predictions from the media source) to the empirical probability (the results from the experiment).

Question: 3

a. Using the data from the public opinion poll experiment, the numbers of trials in a binomial probability experiment would be 100, the number of successes would be 40 (based on the 0.4 probability of supporting Candidate A), and the number of failures would be 60.

b. Results of the experiment could be the number of successes out of 100 trials, for example 40 out of 100.

c. The difference between the empirical and theoretical probabilities would be the difference between the predicted percentage of support and the actual percentage of support found in the experiment. Trends in the outcomes could be observed by looking at the overall success rate and comparing it to the predicted probability.

THIS IS WHAT I NEED HELP WITH!!

Welcome to the Discussion Boards.

Respond to the following discussion prompts. Number your responses.

2. Did you use the fundamental counting principle or combinations in your project? Explain how and why you did or did not.
4. How did you use modeling in your project?