Case Study: Election Results When An Election

Titleabc123 Version X1case Study Election Resultswhen An Election F

When an election for political office takes place, the television networks cancel regular programming and instead, provide election coverage. When the ballots are counted, the results are reported. For important offices such as president or senator in large states, the networks actively compete to see which will be the first to predict a winner. This is done through exit polls, where a random sample of voters who exit the polling booths is asked whom they voted for. From the data, the sample proportion supporting each candidate is computed.

Hypothesis testing is employed to determine whether there is sufficient evidence to infer that a particular candidate will receive enough votes to win. During the 2000 Florida elections, pollsters recorded votes for the two leading candidates: Democrat Al Gore and Republican George W. Bush. In a sample of 765 voters, 358 votes supported Gore, while 407 supported Bush.

The networks declare a winner if a candidate obtains more than 50% of the votes. Since polls close at 8:00 P.M., the question is whether the networks should announce Bush as the winner at 8:01 P.M. based on the sample data. Using a significance level of 0.10 (α), conduct a one-sample hypothesis test to determine if the data supports the prediction that George W. Bush will win Florida in 2000.

Paper For Above instruction

Introduction

The 2000 United States presidential election was one of the most contentious and closely contested in American history. The role of exit polls and statistical hypothesis testing became critical in predicting the winner in real-time as votes were still being tallied. Specifically, in the state of Florida, the question arose whether network analysts could reliably predict George W. Bush's victory based on early exit poll data and sample proportions. This paper aims to perform a hypothesis test for the sample data collected during the Florida election of 2000, to assess whether the evidence was sufficient to declare Bush the winner at 8:01 P.M., based on the sample results obtained immediately after polls closed.

Background and Data Description

During the Florida election, a sample of 765 voters was surveyed, with 358 supporting Al Gore and 407 supporting George W. Bush. The primary focus is to determine if Bush's proportion of votes in the sample exceeds 50%, which would imply he is likely to win the election. The sample proportion supporting Bush (p̂) was calculated as 407/765 ≈ 0.532. The hypothesis test will evaluate whether this proportion significantly differs from 0.50, indicating a genuine lead in voter support.

Methodology: Hypothesis Testing Framework

The hypothesis testing approach involves setting up null and alternative hypotheses:

• Null hypothesis (H₀): p = 0.50, meaning Bush has exactly 50% support in the population.
• Alternative hypothesis (H₁): p > 0.50, indicating Bush's support exceeds 50% and he is likely to win.

This test is a one-sided z-test for proportions, suitable given the large sample size, which allows for the approximation to normality (Zar, 2010). The test statistic is calculated as:

Z = (p̂ - p₀) / √[p₀(1 - p₀) / n]

where p̂ is the sample proportion, p₀ is 0.50, and n is the sample size.

Using the data, Z = (0.532 - 0.50) / √[0.50(0.50) / 765] ≈ 2.16. Comparing this Z-value to the critical value at α = 0.10, which is approximately 1.28, the computed Z exceeds the critical value, suggesting statistical significance.

Results: Statistical Analysis

Calculations show that the Z-statistic is approximately 2.16. Since 2.16 > 1.28, we reject the null hypothesis at the 10% significance level. This indicates that there is statistically significant evidence supporting the claim that Bush's support in the sample exceeds 50%, and thus, the network analyst has valid grounds to predict Bush as the winner based on this sample.

Furthermore, the p-value associated with Z = 2.16 is approximately 0.015, which is less than 0.10, reinforcing the conclusion that the support for Bush is significantly greater than 50%.

Implications and Conclusion

The statistical analysis provides strong evidence that George W. Bush was likely to win Florida based on the sample data collected immediately after the polls closed. Consequently, the networks had a reasonable basis to announce Bush as the winner at 8:01 P.M., just one minute after the polls closed. This demonstrates the practical utility of hypothesis testing in election forecasting, especially when quick decisions are necessary in live broadcast scenarios (Moreira & Hastie, 2001). Nonetheless, it is important to consider the sampling variability and potential biases inherent in exit polls before making definitive claims (Lau, Sigelman, & Rovner, 2007).

Overall, the hypothesis test confirms that the early sample data was statistically significant in predicting the outcome, affirming the importance of inferential statistics in political and electoral analyses.

References

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