Case Study: Election Results For Political Office

Question

Case Study Election Resultswhen An Election For Political Office Tak Case Study – Election Results 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. However, 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, wherein a random sample of voters who exit the polling booth is asked for whom they voted. From the data, the sample proportion of voters supporting the candidates is computed. Hypothesis testing is applied to determine whether there is enough evidence to infer the leading candidate will garner enough votes to win. Suppose in the exit poll from the state of Florida during the 2000 year elections, the pollsters recorded only the votes of the two candidates who had any chance of winning: Democrat Al Gore and Republican George W. Bush. In a sample of 765 voters, the number of votes cast for Al Gore was 358 and the number of votes cast for George W. Bush was 407. The network predicts the candidate as a winner if he wins more than 50% of the votes. The polls close at 8:00 P.M. Based on the sample results, conduct a one-sample hypothesis test to determine if the networks should announce at 8:01 P.M. that the Republican candidate George W. Bush will win the state. Use 0.10 as the significance level (Î±).

Dr. Jack HW Helper · Accepted Answer

The 2000 United States presidential election in Florida was a critical and highly scrutinized electoral process, with immediate implications for national politics. The networks' rush to declare a winner based on exit polls reflects the urgency and competitive nature inherent in such high-stakes elections. To evaluate these early predictions, statistical hypothesis testing provides a rigorous framework to determine if preliminary results justify announcing the winner before official counts are complete. In this scenario, the key question is whether George W. Bush's support exceeds 50% in the sampled electorate, warranting a declaration of victory. Using the provided data, the sample comprises 765 voters, with 407 votes for Bush and 358 votes for Gore. The sample proportion p̂ (p-hat) for Bush is calculated as: p̂ = 407 / 765 ≈ 0.5314 This indicates that approximately 53.14% of the sampled voters support Bush, suggesting he may be leading nationally and in Florida. The population proportion p represents the true proportion of Bush supporters among all voters in Florida, which is hypothesized to be greater than 0.5 (50%) under the alternative hypothesis. Hypotheses Formulation Null hypothesis (H₀): p = 0.5 (Bush has exactly 50% support; no clear majority) Alternative hypothesis (H₁): p > 0.5 (Bush has more than 50% support) This one-tailed test will evaluate whether there is sufficient evidence to reject the null hypothesis in favor of the alternative at a significance level of α = 0.10. Test Statistic Calculation The z-test for a proportion is used, calculated as: z = (p̂ - p₀) / √[p₀(1 - p₀) / n] where p₀ = 0.5, n = 765, and p̂ ≈ 0.5314. Plugging in the numbers: z = (0.5314 - 0.5) / √[0.5 * 0.5 / 765] ≈ 0.0314 / √[0.25 / 765] ≈ 0.0314 / √0.0003268 ≈ 0.0314 / 0.01807 ≈ 1.738 Decision Rule and Conclusion Using standard normal distribution tables, the critical value for a one-sided test at α = 0.10 is approximately 1.28. Since the calculated z-value (1.738) exceeds 1

Case Study: Election Results For Political Office

Case Study Election Resultswhen An Election For Political Office Tak

Paper For Above instruction

Hypotheses Formulation

Test Statistic Calculation

Decision Rule and Conclusion

References