Objective: To apply core probability concepts and contingency table analysis to real-world community data, understand independence between categorical variables, and visually present findings for public understanding.

Your Scenario: Local Government & Citizen Engagement

You are a Data Storyteller for a non-profit called "Empower Local Voices," which aims to improve citizen engagement with local government. Your latest project involves analyzing data from a recent city survey to understand how different groups of residents participate in local decision-making and what their priorities are.

You need to create a visual report (one-pager/infographic) that clarifies key probability concepts using the survey data and presents crucial findings about resident engagement patterns to the public.

Your Data: You can locate the data within StatCrunch under the same title as this assignment "Application Assignment 2: Analyzing Community Decisions & Opinions"

Your Deliverable: "Citizen Engagement Insights" One-Pager/Infographic

Create a single page (or a digital infographic, max 2 pages) that visually summarizes your findings and clarifies key probability concepts. It should be persuasive and easy for local residents to understand. You can use tools like Google Slides, PowerPoint, Canva, Piktochart, or a well-organized Word/Google Doc.

Your One-Pager/Infographic MUST include the following sections/elements:

1. Catchy Title: A clear and engaging title for your report (e.g., "Understanding Our City's Voice: Engagement & Preferences").
2. Probability Basics Explained (for the Public):
   
   • Choose one simple event from your data (e.g., "a resident is in the 'Over 50' age group").
   • Calculate its Empirical Probability based on your sample data.
   • Explain to a layperson (e.g., in a small text box on your infographic):
     
     • What is an "Outcome" and "Sample Space" in the context of this survey?
     • What is Empirical Probability (using your chosen event as an example)?
     • What is a Complementary Event (using your chosen event as an example) and how would you calculate its probability?
3. Cross-Tabulation & Joint/Marginal Probabilities:
   
   • Use StatCrunch to create a Contingency Table(Frequency Table) for "Age_Group" (Row Variable) by "Engaged_in_Last_Election" (Column Variable). Include this table on your one-pager.
   • From this table, present the following probabilities for a randomly selected resident:
     
     • Marginal Probability: Find the probability that someone engaged in the last election. Give as a properly rounded decimal. 
     • Joint Probability: Find the probability that they did not engage in the last election and were under 30 years old. Give as a properly rounded decimal. 
   • Insights: What do these probabilities tell "Empower Local Voices" about overall engagement and specific age group involvement?
4. Conditional Probability in Action:
   
   • Using your contingency table from Section 3, calculate the following conditional probability: that someone who is over 50 engaged in last election. Give as a properly rounded decimal. 
   • Explain what this conditional probability meansin plain language. Why might a local government official be particularly interested in this specific conditional probability (instead of just the overall marginal probability of engagement)?
5. Testing for Independence (Chi-Square Test):
   
   • Use StatCrunch to perform a Chi-Square Test for Independence on the "Age_Group" and "Engaged_in_Last_Election" variables. Include the p-value from your StatCrunch output on your one-pager.
   • Hypotheses: State the Null Hypothesis (Ho) and Alternative Hypothesis (Ha) for this test.
   • Conclusion: Give the p-value from StatCrunch and  state whether you find evidence of independence or dependence between Age_Group and Engagement in the Last Election, given a significance level of α=0.05.
   • Implications: What does this conclusion mean for "Empower Local Voices" and their strategies for encouraging participation? (e.g., Do they need targeted strategies for different age groups, or a more general approach?)
6. Ethical Consideration & Law of Large Numbers:
   
   • Ethical Reflection: This pilot survey has a limited sample size of 200. Briefly explain one potential ethical concern related to making major policy decisions based only on the results of such a small survey.
   • Law of Large Numbers: If "Empower Local Voices" were to conduct a much larger survey (e.g., 20,000 residents), how would the Law of Large Numbers apply to the empirical probabilities they calculate (like the probability of "Engaged_in_Last_Election = Yes")?