Simulation-Based Exploration of Statistical Inference: CLT, Statistical Power, Chi-Square Tests and P-Value Computation Using R

This report presents a simulation-based exploration of fundamental concepts in statistical inference using the R programming language. Five projects are developed to investigate the Central Limit Theorem, Type II error and statistical power, power analysis and sample-size determination, chi-square tests for independence and homogeneity, and manual computation of p-values for discrete and continuous distributions. Simulation experiments are used to examine theoretical results empirically, visualize sampling distributions, investigate the effects of sample size and effect size on statistical power, and verify manually derived results against R's built-in statistical functions. The report emphasizes computational experimentation as a means of developing intuition for statistical inference and demonstrates reproducible implementations using R.