Calculo del Tamaño de la Muestra para Poblaciones finitas e Infinitas
Summary
TLDREl script del video enseña cómo calcular una muestra representativa para analizar el mercado objetivo. Define la muestra, destaca su importancia para estimar características de la población y explica técnicas de muestreo probabilístico y no probabilístico. Profundiza en fórmulas para calcular tamaño de muestra en poblaciones infinitas y finitas, usando ejemplos prácticos. Finalmente, motiva a identificar el mercado objetivo y a realizar encuestas para estimar la demanda y la factibilidad de un negocio.
Takeaways
- 🔍 La importancia de la muestra representaativa radica en su capacidad para realizar análisis fiables sobre una población a través de un subconjunto seleccionado.
- 📊 Las técnicas de muestreo permiten obtener una muestra que sea representativa de la población general, lo que permite aplicar los resultados a toda la población.
- 🎯 El muestreo no probabilístico es común en evaluaciones de proyectos empresariales, permitiendo seleccionar individuos con características deseadas para ser consumidores potenciales.
- 📚 Existen dos técnicas principales de muestreo en sociología: probabilístico y no probabilístico, siendo el primero más sistemático y equitativo.
- 🌐 Las poblaciones finitas son aquellas que se conocen a través de censos y estadísticas oficiales, mientras que las poblaciones infinitas son difíciles de determinar y no se cuentan fácilmente.
- 📉 El cálculo del tamaño de la muestra representa para poblaciones infinitas se realiza a través de una fórmula que involucra el nivel de confianza, la probabilidad de éxito y el error de muestreo aceptable.
- 📌 El nivel de confianza (90%, 95%, 99%) determina el coeficiente Z, siendo 1.96 el valor común para un 95% de confianza.
- 📐 Para poblaciones finitas, se utiliza una fórmula diferente que incluye el tamaño de la población total y ajusta el tamaño de la muestra en consecuencia.
- 📝 Un ejemplo práctico muestra cómo calcular el tamaño de la muestra para una tienda de zapatos femeninos, considerando un nivel de confianza y un error de muestreo aceptable.
- 🎯 Al conocer el tamaño de la población, se puede realizar un muestreo más preciso y ajustado a las necesidades del negocio, asegurando una representatividad adecuada.
- 📈 La identificación del mercado objetivo es crucial para aplicar encuestas y obtener datos significativos, lo que puede ser complementado con información adicional en recursos en línea.
Q & A
¿Qué es una muestra en el contexto de un estudio estadístico?
-Una muestra es una parte o conjunto de cosas, personas o datos que se consideran representativos de una población y que se separan con el propósito de someterlos a estudio, análisis o experimentación para obtener resultados lo más fiables posibles.
¿Por qué es importante calcular correctamente la muestra en un estudio?
-Es esencial calcular correctamente la muestra porque a través de ella podemos realizar análisis de situaciones de una empresa o de cualquier ámbito de la sociedad, lo que nos permite estimar características de la población como densidad, tamaño, distribución de edad, tasa de crecimiento, sexo, etc.
¿Cuáles son las dos técnicas principales de muestreo en sociología?
-Las dos técnicas principales de muestreo en sociología son la probabilística, donde los sujetos de la muestra son elegidos de acuerdo con probabilidades conocidas como sistemática, muestreo aleatorio simple, estratificado y conglomerado; y la no probabilística, donde los individuos son elegidos sin tener en cuenta su probabilidad de ocurrencia de manera subjetiva.
¿Qué tipo de muestreo se utiliza en las evaluaciones de proyectos empresariales y por qué?
-Se utiliza el muestreo no probabilístico en las evaluaciones de proyectos empresariales porque permite seleccionar individuos que mejor se ajusten a ser consumidores potenciales de nuestros productos o servicios.
¿Qué son las poblaciones finitas e infinitas y cómo se diferencian?
-Las poblaciones finitas son aquellas que conocemos a través de censos, estadísticas, datos oficiales publicados en la web, etc., mientras que las poblaciones infinitas son aquellas que son difíciles de determinar, como los insectos en el planeta o la basura en un país.
¿Cómo se calcula el tamaño de una muestra representativa si no se conoce la población (población infinita)?
-Se utiliza la fórmula n = Z² * (p * q) / E², donde n representa el tamaño de la muestra, Z es el nivel de confianza deseado, p es la probabilidad de éxito, q es 1 - p y E es el error de muestreo aceptable.
¿Cuál es el nivel de confianza comúnmente utilizado en los estudios y por qué?
-El nivel de confianza comúnmente utilizado en los estudios es del 95%, representado por un Zα de 1.96, ya que ofrece un buen balance entre la precisión del estudio y el tamaño de la muestra requerida.
¿Cómo se calcula el tamaño de una muestra representativa si se conoce la población (población finita)?
-Se utiliza la fórmula N = (N * Z² * p * q) / (E² * (n - 1) + Z² * p * q), donde N es el tamaño de la población, y los demás símbolos tienen el mismo significado que en la fórmula para poblaciones infinitas.
¿Cómo se determina el tamaño de la muestra para un negocio de zapatos para mujeres sin una población específica?
-Se asume una población infinita y se utiliza la fórmula n = Z² * (p * q) / E² con Zα de 1.96 para un 95% de confianza, p de 0.5 (probabilidad de éxito) y E del 5% como error de muestreo aceptable, lo que resulta en una muestra de 384 mujeres.
Si se tiene una población específica de 430,000 mujeres y se desea calcular la muestra para un negocio de zapatos, ¿cómo se hace?
-Se utiliza la fórmula para poblaciones finitas, asumiendo un Zα de 1.96 para un 95% de confianza, p de 0.7 (probabilidad de éxito) y E del 5%, lo que resulta en una muestra de 322 mujeres.
¿Cómo se puede estimar el tamaño de la población objetivo para un negocio antes de realizar un estudio de mercado?
-Se puede estimar a través de estadísticas oficiales, censos, publicaciones en la web, o conociendo la cantidad de clientes de competidores, su volumen de ventas, unidades vendidas o número de visitas diarias, para aplicar estrategias de marketing y estimar qué porcentaje de ese mercado se puede capturar.
Outlines
🔍 Introducción a la Muestra Representativa
El primer párrafo introduce el concepto de muestra y su importancia en la investigación de mercados. Se define una muestra como una parte representativa de una población, utilizada para el análisis y experimentación con el fin de obtener resultados fiables. Destaca la relevancia de calcular adecuadamente la muestra para estimar características de la población, como la distribución por edad, tasa de crecimiento, sexo, etc. Se mencionan las técnicas de muestreo probabilístico y no probabilístico, y se enfatiza la elección del muestreo no probabilístico para evaluaciones de proyectos empresariales debido a su capacidad para seleccionar a individuos con mayor potencial de ser consumidores.
📚 Cálculo del Tamaño de la Muestra Representativa
El segundo párrafo se enfoca en el cálculo del tamaño de la muestra representativa, explicando las fórmulas para poblaciones infinitas y finitas. Se describen los componentes de la fórmula, como el nivel de confianza (Z), la probabilidad de éxito (p), la probabilidad de fracaso (q) y el error de muestreo aceptable (E). Se proporciona un ejemplo práctico de cómo calcular el tamaño de la muestra para una tienda de zapatos femeninos, asumiendo una población infinita y un nivel de confianza del 95%, resultando en una muestra de 384 mujeres.
📉 Aplicación de la Fórmula para Poblaciones Finitas
El tercer párrafo continúa con el tema del cálculo del tamaño de la muestra, pero enfocado en poblaciones finitas. Se aplica la fórmula para una población de 430,000 mujeres en un estado, asumiendo un 70% de probabilidad de éxito y un error de muestreo del 5%, resultando en una muestra de 322 mujeres. Además, se discute la identificación del mercado objetivo y cómo se puede estimar el tamaño del mercado utilizando información demográfica y de competidores, así como la importancia de las aproximaciones en la definición de la población objetivo.
Mindmap
Keywords
💡Muestra representativa
💡Análisis de mercado
💡Técnicas de muestreo
💡Muestreo probabilístico
💡Muestreo no probabilístico
💡Población de estudio
💡Poblaciones finitas e infinitas
💡Tamaño de la muestra
💡Nivel de confianza
💡Error de muestreo aceptable
💡Identificación del mercado objetivo
Highlights
Define what a sample is and its purpose in representing a population for study and analysis.
The importance of correctly calculating a sample for reliable analysis and estimation of population characteristics.
Introduction to sampling techniques and their role in obtaining representative samples from a population.
Explanation of probabilistic sampling methods including systematic, simple random, stratified, and conglomerate sampling.
Description of non-probabilistic sampling, where selection is subjective and based on specific characteristics.
The use of non-probabilistic sampling in business project evaluations to select potential consumers.
Differentiation between finite and infinite study populations and their respective examples.
Formula for calculating the size of a representative sample from an infinite population.
Explanation of the Z-score and its relation to confidence levels in sample size calculations.
Assumption of a 50% success probability when no prior data is available for sample size calculation.
The concept of acceptable sampling error and its impact on the precision of a study.
Application of the sample size formula with an example of a shoe store for women.
Calculation of the sample size for a finite population with a known population size.
Example calculation for a shoe store considering the local market population of women.
Importance of understanding the target market for effective survey application and business feasibility.
Guidance on identifying the target market and obtaining population statistics for business planning.
Strategies for estimating market size and potential profitability through competitor analysis.
Invitation to visit mundogerencia.com for additional resources and information on successful business practices.
Transcripts
In this video we will see… How to calculate the representative sample
to analyze your target market. First of all it is worth defining what is a sample
The sample is a part or set of things, people, or data
that are considered to be representative of a population and
is separated with the purpose of subjecting them to study, analysis or experimentation to
get results as reliable as possible
Importance of the samples. To correctly calculate the sample is essential
because through it we can make analysis of situations
of a company or of any field of society easily, It allows us to estimate
the characteristics of the population that the differences of others such as: density or size,
age distribution, growth rate, sex, etc. The sampling techniques
allow us to obtain a representative sample of the general population,
that is, the results of a sample can be applied
or is equivalent to the results of an entire population.
Lets us focus on a small group or target of the market
to obtain data points and special interest. It is a practical way of
segmenting a target into smaller parts. Types of sampling: In sociology,
there are two main techniques of sampling.
The probabilistic, which is where the subjects of the sample are elected in accordance
with probabilities known as the systematic, simple random sampling,
stratified, and the conglomerate; therefore, all elements of
the population have an equal chance of being chosen. The non-probability
where individuals are elected without taking into account
its probability of occurrence, that is to say, in a subjective (Value judgments
by drifting with the feelings or desired characteristics of the individual)
With respect to the above, the type of
sampling used in evaluations of business projects is the
non-probabilistic because that is going to allow us to select individuals who
best suit to be a potential consumer of our products or services.
Types of study population. It should be noted that any study
is carried out on a population, where you must select a proportion or sample
of the same in order to be studied and apply the results
to the totality and issue conclusions about that population.
There are finite and infinite populations where the finite populations
are those that we know from censuses, statistics,
official data published by the web, etc. and infinite populations are those that are difficult
to determine. Example: Infinite populations: populations that do not know
or that we do not find easily the information, among them are: *insects on the planet.
*Trash on the planet or a country. *Quantity of sand on the beach.
*students worldwide *Number of people who buy bread at the global level.
*Number of red blood cells in the human body. *Number of children who are born daily.
*Number of people who die daily. The finite populations: are populations
that we can find in Statistics, Census, publications on the web etc. or that are easily
determined, examples of these are: *Quantity of roses in a garden
*People in a country, region, state, city, town, place, Etc.
*Companies in a place, region, area, Etc. *products produced in x company.
*Children in a school. *Women in a state or city
*Children under the age of 10 years in a city. Etc. Now, let's get to the main objective
of this video. How to calculate the size of the representative sample is calculated
through the application in any of the following formulas:
If you do not know the population, that is to say, infinite population, the formula would be
N is equal to Z to the square by p to q, q would be 1-p between E squared. n = represents the sample size.
Z represents the desired confidence level. (It chooses
the investigator depending on how much certainty you want in the investigation).
According to the different levels of confidence the coefficient Z varies as follows
(data obtained from the table of normal distribution):
*For a security level of 90 per cent Zα is going to be = 1.64
*For a security level of 95 per cent is = 1.96 zα
*For a security level of 99%= 2.57 coefficient Zα Voucher
P = probability of success. (If you have past research
you will have an idea of how much success rate has to be
the event happens, in case you do not know then placed which is a 50%,
that is to say, that may or may not happen.) 1 - p = Q or probability of failure
(that is, if p = 40% then q= 100% - 40% = 60%
What is lacking to reach the 100%)
E = acceptable sampling error. The investigator chooses depending on
how much error percentage is willing to assume. If you know the amount of population,
that is to say (finite population) The formula to be applied is the following:
N is equal to N capital letter by Z to the square by p by q, between e squared,
for n-minus 1 more Z to the square by p for q
where N a capital letter is the population. For a better understanding of this calculation
we will apply a case example: infinite population
Suppose you want to mount a shoe store for women but not specified in that place will be the business,
we just want to know how many women
interviewed to determine our demand. In this case the formula
that we would be infinite population. Where: n = sample size.
Is the value you want to obtain. Z= desired confidence level.
The confidence level of the sample will determine between 90%, 95% and 99%
(the higher this level of trust, the higher the sample, therefore,
when not specified as a percentage required, always choose
an intermediate at this level) and it is common to choose a level of 95%... or a security level
of 95 per cent Zα= 1.96. ACCORDING TO THE TABLE OF NORMAL DISTRIBUTION
P = probability of success.
The expected proportion assumes a 50% because it maximizes the sample size.
This value is assumed when you do not know what is the probability of success of the analysis.
If you want to know this value or calculate it apart it is necessary
to perform some test to determine surveys and obtain the standard deviation of the study.
1 - p = Q or probability of failure
in this case as P is equal to 50% then q= 50% to complete the 100%
E = acceptable sampling error. The precision that we wish
for the study is of a 5% (i.e., reduce the sampling error).
This is the standard used in the investigations. The acceptable range is 1% to 9%
We will apply then the formula according to our example
by replacing each letter by the corresponding numbers
we get the following calculations: 1.96 squared, by 0.5, by 1 minus 0.5, between 0.05 to the square.
1.96 to the square is 3.8416, by 0.5, by 1 less than 0.5. .. 1 less than 0.5 is 0.5,
between 0.05 to the square is 0.0025...
By multiplying the two numerators, 3.8416 by 0.25, is equal to 0.9604 Between 0.0025
Results n is equal to 384.16 rounded up 384
The result tells us that we should interview or survey to
384 women (rounding the result always)
to obtain a representative result of the market population of shoe store
with a 95% security. Now we want to know how many women
apply the surveys to perform the analysis on the same shoe store for ladies.
We have to the population of women in the state where the business is of
430,000 women, that represents our population, because
we will focus to begin in the local market. In this case we indicate a
probability of success of 70%. Then the data we have are: n = sample size.
Uppercase N = population size 430,000 .
How we do not specify what level of trust has the study we will use the same indicators
as in the case of infinite population.
Z= desired confidence level. 95% i.e. 1.96 p = probability of success.
They say that it is 70% or 0.7 in relative number
q= probability of failure. It is 1 - 0.70 = 0.3 it would be in percentage 30%
e = acceptable sampling error. 5%.. We already know that this value can be known through the statistics
or censuses carried out by the entities of the Government or by the chambers of
the country. Also by specialized magazines, or by studies conducted
earlier in the company, or its trend of previous years view
in the statistics of the company. But as we do not specify
we choose the base 5%. We apply then the formula by replacing each letter by its value:
And with the help of the calculator we obtain that N is equal to
322.45, rounding, 322, that is to say, that in this case minimum must be interviewed
322 women to get our result representative of the population.
To know the approximate size of the market in which to offer their
service ensures that the business is potentially profitable.
With the sample calculated will be able to conduct surveys to our target market and perform
the following calculations of feasibility of the business.
Now it remains to detect our target market in order to know who we must apply the survey.
Remember that we mentioned earlier that the studies of business apply in the
non-probabilistic sampling. This is easy.
In the link in the description will take them to the blog entry complementary to this video
where you will see how to identify our target market in addition
to a guide to download for free where he offers tips to develop your effective survey material
Once having defined the target market should be sought in
the statistics of the country the amount of population in the current year
and see it broken down by states or cities. Example to detect our population;
assume the total population of the country X is, between men and women = 30 million inhabitants
of which 16 million are women. Of those 16 million women,
430,000 are in the State X.
00,000 women according to survey, buy shoes at least once a year 1.
There are 10 shops in the state of shoes unisex, which seems reasonable to aspire to capture
the 5% of the local market, being 100,000*5% = 5,000 women who purchase
in our business as sales target for the first year.
So are going by calculating and estimating the size of the population.
Remember that you know the size of the population that has a business is never going to be
exactly accurate, you are always working with approximations.
Another way is by knowing the amount of customers of competitors,
its annual turnover, units sold or amount of daily visits,
to get an estimate of how much of that percentage we can catch us by
applying marketing strategies. These values are difficult to obtain,
but there are companies that sell financial information from other companies.
If you want to dig deeper on this topic I invite you to visit our website mundogerencia.com.
There you will find additional information guides, collectibles, tools,
and much more. Visit us. Equally, I invite
you to subscribe and follow us on our social networks to keep you up to date of our publications.
Enables notification so you don't miss out on any of our video channel.
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