Election Analytics Mastery

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What this quiz asks

1. In a simple random sample (SRS) of 400 voters from a population of 10,000, what is the probability that any single individual voter is selected for the poll?
2. A pollster uses stratified sampling, dividing 2,000 voters into two groups: 1,200 urban and 800 rural. If they need a total sample of 200, how many rural voters should be selected to ensure proportional representation?
3. A researcher conducts a cluster sample by selecting 5 precincts out of 50 total precincts. If each precinct has an average of 400 voters, what is the total number of voters covered by this sampling methodology?
4. To achieve a 95% confidence level in a poll, the required sample size n is determined by n = (Z² * p * (1-p)) / E². If Z=1.96, p=0.5, and E=0.05, what is the required sample size n?
5. In a simple random sample of 400 voters, the proportion favoring a candidate is 0.52. Calculate the margin of error at a 95% confidence level (z-score = 1.96) using the formula ME = z * sqrt(p(1-p)/n).
6. A poll reports a candidate leads with 48% and a margin of error of ±3.5%. What is the range of the confidence interval for the candidate's support?
7. To halve the margin of error of a poll, by what factor must the sample size (n) be increased, assuming the proportion (p) and confidence level remain constant?
8. If a survey of 1000 people has a margin of error of 3.1%, what would the margin of error be if the sample size were increased to 4000, assuming p=0.5?
9. In a polling sample of 400 likely voters, 200 support Candidate A. Calculate the standard error of the proportion (SE) to determine the foundation for a 95% confidence interval.
10. Given a sample proportion of 0.52 and a margin of error of 0.03, what is the lower bound of the 95% confidence interval for the population support?
11. If the standard error is 0.02 and the critical value (z*) for a 95% confidence interval is 1.96, what is the margin of error (ME)?
12. A poll reports 55% support for a candidate with a margin of error of ±3%. Which values fall within this 95% confidence interval?
13. A poll samples 400 people from a population where 60% are Group A and 40% are Group B. If the actual population composition is 50% Group A and 50% Group B, what weight should be applied to each respondent in Group B to correct for sampling bias?
14. A polling firm surveys 1000 voters. The sample shows 55% support Candidate X, but the population is 52% male and 48% female. If the sample is 60% male and 40% female, what weight multiplier should be applied to female respondents to achieve a representative balance?
15. In a survey of 2000, 1200 are aged 18-34 and 800 are 35+. The true population is 40% aged 18-34 and 60% aged 35+. What are the weights for the 18-34 and 35+ groups respectively?
16. A poll finds 50% support for a policy. The sample is 70% urban (true population 50% urban) and 30% rural (true population 50% rural). If the urban support is 60% and rural support is 20%, what is the weighted support for the policy?
17. A pollster tests the null hypothesis H₀: p = 0.50 against Hₐ: p ≠ 0.50. Given a sample proportion p̂ = 0.54 with a standard error SE = 0.02, calculate the Z-score for this hypothesis test.
18. In a hypothesis test for an election, the calculated p-value is 0.038. Using a significance level (α) of 0.05, which of the following conclusions is statistically valid?
19. A researcher conducts a two-tailed test for a candidate's support. The test statistic is 2.58. If the critical Z-value for α=0.01 is 2.576, what is the correct decision regarding the null hypothesis?
20. A poll claims a candidate has 50% support. In a sample of 400 voters, 220 support the candidate. Calculate the standard error SE = √[p(1-p)/n] using p=0.5 and n=400 to determine if the sample proportion is statistically significant.
21. In a predictive model for a two-candidate election, the probability of Candidate A winning is modeled by a logistic function P(x) = 1 / (1 + e^(-k(x-x₀))), where x is the current polling percentage lead. If k = 0.5 and the threshold x₀ = 0, what is the probability of winning if the current lead x = 2%?
22. A campaign uses a Bayesian update model to predict the probability of winning. If the prior probability is 0.40 and the likelihood of observing current positive polling data is 0.70, while the probability of observing such data regardless of winning is 0.50, what is the posterior probability?
23. In a linear regression model for predicting vote share (Y) based on economic growth (X), the equation is Y = 0.5X + 30. If economic growth is projected to be 4%, what is the predicted vote share, and what is the residual if the actual result is 35%?
24. A Monte Carlo simulation runs 10,000 trials to predict an election outcome. If Candidate A wins in 6,200 of those trials, what is the estimated win probability, and what is the standard error of this proportion?

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