ESTADÍSTICA INFERENCIAL - Tamaño Muestral: Z-Score (Estandarización)

This session revisits the practical example of a coin toss to further illustrate empirically how the relative frequencies of multiple limited samples shape the sampling error of the denominator. The class then focuses on the Z-score parameter in the context of unadjusted sample size. The logic of parametric standardization is explained, starting with deviations from the population mean divided by the standard deviation, which allows any variable to be transformed into a normal distribution with a mean of zero and a variance of one. Using the empirical rule, the session analytically details why the exact critical values ​​of Z-scores—such as 1.65, 1.96, and 2.57—are mathematically located slightly below the integers of the standard deviations to meet the confidence levels of 90%, 95%, and 99%, respectively. Table of Contents: 0:00:00 – Introduction and recap of the parameters $P$ and $E$. 0:01:10 – Empirical simulation with relative frequencies and multiple samples of limited size ($n=10$). 0:03:42 – Sampling error conceived as the average of the observed relative frequencies. 0:04:25 – Presentation of the formula for unadjusted sample size (infinite population). 0:05:08 – Mathematical definition and formal calculation of the $Z$-score in a parametric environment. 0:06:09 – Geometric derivation of standardization and properties of the standard normal distribution $N(0,1)$. 0:07:20 – Graphical representation of deviations in standard deviation units on both sides of the mean. 0:08:42 – Usefulness of standardization as a universal language for variables with different units of measurement. 0:09:36 – Explanation of the empirical rule of the normal distribution and data coverage in the tails. 0:10:44 – Identification of outliers outside the three standard deviation range. 0:12:05 – Analytical relationship between the confidence level and significance ($\alpha$). 0:13:40 – Derivation of the exact critical values ​​of $Z$: correspondence for 99%, 95%, and 90% confidence levels. 0:15:21 – Closing of the video and introduction of the adjustment for finite populations in the next session. #InferentialStatistics #SampleSize #ZScore #Standardization #NormalDistribution #ConfidenceLevel #StatisticalSignificance #Sampling