ESTADÍSTICA INFERENCIAL - Tamaño Muestral: Error Muestral (e)

In this session, we advance the analytical and parametric deconstruction of the sample size formula for infinite populations. The video begins by completing the algebraic development of the variance of a Bernoulli variable, demonstrating step by step its factorization as $p(1-p)$. Subsequently, the core of the lesson focuses on explaining the intuition behind the Sampling Error ($e$). Through the analogy of a coin toss, the asymptotic behavior guided by the Law of Large Numbers and the Central Limit Theorem is intuitively introduced. It details how the gap between the observed and theoretical values ​​(the error) decreases as the sample size increases. Finally, the structure of the unadjusted sample size formula is formally presented, highlighting why all its components ($Z^2$, $e^2$, and the variance) are expressed in quadratic terms. Table of Contents: 0:00:00 – Introduction and review of sample size parameters. 0:00:45 – Analytical differentiation of squared terms in expected value operators. 0:01:46 – Factorization and final expression of the variance of a Bernoulli variable ($p(1-p)$). 0:02:44 – Introduction and conceptual definition of Sampling Error ($e$). 0:03:15 – Intuition of sampling error through the example of a coin toss. 0:04:41 – Empirical relationship: repeated samples of equal size within a population. 0:06:45 – Intuitive explanation of the Law of Large Numbers and the Central Limit Theorem. 0:07:35 – Analysis of the gap between the theoretical and empirical values. 0:08:23 – Sampling error analytically conceived as an average of sample differences. 0:09:36 – Theoretical clarification: Sample vs. Sample size. 0:11:40 – Empirical criteria and common conventions in practice (Use of a 5% error). 0:13:01 – Formal presentation of the sample size formula for infinite populations. 0:14:11 – Justification for the use of quadratic terms in the formula and non-negativity properties. 0:14:53 – Closing remarks and preview of the next parameter to be studied ($Z$-score). #InferentialStatistics #SampleSize #SamplingError #BernoulliVariable #LawOfLargeNumbers #CentralLimitTheorem #StatisticalSampling #Econometrics #StatisticalInference