Problem Set 9 Is Due On Friday, November 20

Problem Set 9this Problem Set Is Due On Friday November 20th End Of Da

Identify the actual assignment questions: The prompt contains multiple exercises related to hypothesis testing, regression analysis, and data interpretation, based on datasets involving polling results, violence in Chechnya, minimum wage effects, UK campaign spending, and statistical concepts. The core tasks include performing hypothesis tests with z-scores, analyzing treatment effects using different estimators, conducting regression analyses with confidence intervals, and answering conceptual questions about statistical assumptions and inference.

Paper For Above instruction

Hypothesis testing and statistical inference are fundamental tools in analyzing empirical data across various fields, from political polling to conflict studies and economic policy. This paper synthesizes approaches to hypothesis testing in polling results, the effect of violence on insurgent attacks, the impact of minimum wage hikes, and campaign spending effects, alongside conceptual discussion on statistical assumptions and inference principles.

In the context of political polling, the null hypothesis often pertains to the proportion of voters supporting a candidate. For instance, in analyzing polls from Florida, Virginia, Pennsylvania, North Carolina, and Iowa during the 2016 U.S. presidential election, we employ z-scores to test whether observed proportions significantly differ from hypothesized values. The test involves computing the z-statistic as (p̂ - p₀) / √(p₀(1 - p₀)/n), where p̂ is the sample proportion, p₀ is the hypothesized proportion, and n is the sample size. The critical value for a 5% significance level (two-tailed) is approximately ±1.96. If the computed z exceeds this threshold in magnitude, the null hypothesis is rejected.

For example, a Florida poll with 884 voters and 45% support for Trump (p̂=0.45) tested against a null hypothesis of p₀=0.4902 yields a z-score of approximately -1.65, which does not exceed ±1.96, indicating insufficient evidence to reject the null at the 5% level. Conversely, testing against p₀=0.42 leads to a z-score of about 2.10, suggesting rejection of the null hypothesis which states that Trump would obtain 42% of the FL vote at the 5% significance level.

Similar procedures apply for the Virginia, Pennsylvania, North Carolina, and Iowa polls, where z-scores are compared to critical values. These tests illuminate whether the polling data provide statistically significant evidence that support differs from hypothesized values, informing political strategies and understanding voter behavior.

In conflict studies, particularly analyzing Russian artillery fire in Chechnya, various estimators assess the causal effect of indiscriminate violence on insurgent attacks. The Difference-in-Means (DiM) estimator compares mean attack counts between shelling and non-shelling villages, assuming independence and identical distribution of observations. The null hypothesis posits that the Population Average Treatment Effect (PATE) equals zero, indicating no effect of shelling on insurgent activity. Using linear regression, the DiM can be estimated as the coefficient of the treatment variable fire in the model postattack = α + βfire + ε, where β represents the treatment effect. Statistical significance is assessed via the standard error and the corresponding z-score or t-statistic.

The Before and After (BA) estimator considers pre- and post-attack attack rates within the same villages, while the difference-in-differences (DiD) approach combines both, controlling for confounding factors. Each estimator tests the null hypothesis PATE=0, determining whether artillery shelling incites or suppresses insurgent attacks. The statistical significance of these effects depends on the estimated coefficient, its standard error, and the chosen significance level, typically 5%. Confidence intervals further provide a range of plausible effect sizes, informing policy implications regarding military strategies and civilian safety.

Regarding economic policy, specifically minimum wage effects, hypothesis testing involves comparing the estimated Population Average Treatment Effect (PATE) to hypothesized values (e.g., zero or -0.10). For the difference-in-means estimator, with an estimate of 0.048 and standard deviation 0.034, t-statistics are computed as estimate divided by standard deviation. Comparing this to critical values at significance levels of 1% (±1.64), 5% (±1.96), and 10% (±2.58), reveals whether the effect of minimum wage increases on the proportion of full-time employees is statistically significant. Similar steps apply for the Before and After and Difference-in-Differences estimators.

In analyzing campaign spending data from the UK 2019 elections, regression models estimate the influence of party campaign expenditures on vote shares. The regression includes variables such as spending by different parties, with coefficients indicating their marginal effects. Testing hypotheses about the significance of these effects involves t-tests comparing each coefficient to zero, under a 5% significance level. Confidence intervals obtained via the confint function in R provide additional insight, delineating a range within which the true effect likely resides with specified confidence.

Finally, a comprehensive understanding of statistical inference necessitates familiarity with core assumptions of linear regression, including linearity, independence, homoscedasticity, and normality of residuals. The Central Limit Theorem is pivotal in justifying the use of normal approximations for sampling distributions, especially with large samples. Increasing sample size generally reduces the variance and standard deviation of coefficient estimates, leading to more precise inference. Multicollinearity, particularly high correlation among independent variables, inflates the variance of coefficient estimates, making them unstable and difficult to interpret. Confidence intervals widen as the confidence level increases, reflecting greater uncertainty about the parameter estimates.

References

  • Lyall, J. (2009). Does Indiscriminate Violence Incite Insurgent Attacks: Evidence from Chechnya. Journal of Conflict Resolution, 53(3), 331-362.
  • Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press.
  • Stock, J. H., & Watson, M. W. (2015). Introduction to Econometrics. Pearson.
  • Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
  • Angrist, J. D., & Pischke, J.-S. (2008). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.
  • Stock, J. H., & Watson, M. W. (2007). Introduction to Econometrics (2nd ed.). Pearson.
  • Kennedy, P. (2008). A Guide to Econometrics. Wiley.
  • Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd.
  • Casella, G., & Berger, R. L. (2002). Statistical Inference. Duxbury.
  • R Core Team. (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.

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