Universe, Population, and Sample with Theoretical and Numerical Support

 

Universe, Population, and Sample with Theoretical and Numerical Support

For the research project “Urban Development as a Public Green Area: The Case of Malecón Tajamar,” it is essential to define the universe, population, and sample using both conceptual foundations and empirically supported numerical data.

The universe of the study refers to the total set of elements related to urban development and public green areas in coastal tourist cities. This includes residents, authorities, environmental organizations, and ecosystems across multiple cities facing similar environmental and urbanization challenges. According to Roberto Hernández Sampieri, the universe (or target population in a broad sense) comprises all cases that meet a set of specifications relevant to the research problem. Due to its broad scope and the difficulty of quantifying all elements, the universe is considered large or practically infinite. In methodological terms, this justifies estimating it at more than 1,000,000 individuals, consistent with the criteria for large populations described by Sampieri in research methodology literature.

The population represents a finite and delimited subset of the universe. In this case, it corresponds to the inhabitants of Cancún who are directly or indirectly affected by the development of Malecón Tajamar. As explained by Roberto Hernández Sampieri, the population is the set of all cases that share specific characteristics and from which the sample will be drawn. According to official demographic data from the Instituto Nacional de Estadística y Geografía (INEGI), the municipality of Benito Juárez (Cancún) has an approximate population of 900,000 inhabitants, based on recent census estimates. For analytical purposes, this population may be further refined to those individuals who live near or interact directly with the Tajamar area, resulting in an estimated range between 50,000 and 150,000 individuals, which is acceptable in applied research when geographic delimitation is used.

The sample is a representative subset of the population selected for data collection. According to Roberto Hernández Sampieri, a sample is a subgroup of the population from which data are collected and that should adequately represent it. To determine the appropriate sample size, a statistical calculation was performed using a sample size calculator with the following parameters: a confidence level of 95%, a margin of error of 5%, a population proportion of 50% (used when variability is unknown), and a population size of 150,000. The calculation yields a required sample size of 384 participants, meaning that at least 384 surveys or observations are necessary to ensure that the results reflect the true population values within a ±5% margin of error and with 95% confidence. This result is consistent with the standard statistical formula for large populations:

$n = \frac{Z^2 \cdot p \cdot q}{e^2}$

n=e2Z2⋅p⋅q​

Thus, the sample size of 384 is not arbitrary but is supported both by statistical theory and by the use of a digital sample size calculator, ensuring methodological validity.

In conclusion, the universe, population, and sample in this study are defined through a combination of theoretical criteria proposed by Roberto Hernández Sampieri, official demographic data from INEGI, and statistical calculation tools. This integrated approach ensures that the research on Malecón Tajamar as a public green area is both academically rigorous and methodologically reliable.