BRM UNIT 2 NOTES

Ques 1 What is population and sample with example?

Ans 1 In business research methods, the concepts of population and sample are fundamental to
designing and conducting research. Let's break down these concepts with examples:
Population:
Definition: The population is the entire group of individuals, items, or elements that possess the
characteristics the researcher is studying.
Example: If a company wants to study the job satisfaction of all its employees, the population
would be the entire workforce of that company.
Sample:
Definition: A sample is a subset of the population selected for the actual study. It represents a
smaller group from which the researcher can draw conclusions about the larger population.
Example: In the job satisfaction study mentioned earlier, it might be impractical to survey every
employee in the company. Instead, the researcher could select a representative group, such as a
random sample of 100 employees, to gather data.
Ques 2 What is sampling and sample (Sampling frame ) ?
Ans 2 Sampling:
Sampling is the process of selecting a subset of elements from a larger population to study and
draw conclusions about that population. The goal is to obtain a representative group that
accurately reflects the characteristics of the entire population. Sampling is a practical and
efficient way to conduct research, especially when studying large or diverse populations.
Sample:
A sample is the subset of individuals, items, or data points selected from a population for
inclusion in a research study. It is the group that researchers collect and analyze data from, with
the intention of making generalizations or inferences about the larger population.
Sampling Frame:
A sampling frame is a list or source from which a sample is drawn. It represents the actual
individuals or elements from which the sample will be selected. A well-defined and
comprehensive sampling frame is essential for the validity of the sampling process
Ques 3 What is the difference between Census and sampling ?
Census Example:
Scenario: A government agency aims to collect demographic information from every household
in the country.
Approach: Conducts a census by sending survey forms to every household, requiring each one to
respond.
Sampling Example:
Scenario: A marketing firm wants to assess customer satisfaction for a new product launch.
Approach: Uses a random sampling method to select a representative group of customers for a
satisfaction survey, instead of surveying the entire customer base.
Ques 4 What is sampling size ? What is cover under sampling size selection
(Demographically & Geographically )?
Ans 4 Sampling Size:
Sampling size refers to the number of elements or individuals selected from a population for
inclusion in a research study. It is a critical aspect of the sampling process and impacts the
reliability and precision of study results. The size of the sample should be carefully determined
based on statistical considerations, research objectives, and the characteristics of the population
under study.
Example of sampling size :
Scenario:
A company wants to assess customer satisfaction for a new mobile app among its user base of
10,000 customers.
Sampling Size Determination:
 Objective: Achieve a 95% confidence level with a ±4% margin of error.
 Population Variability: Moderate variability based on past surveys.
 Resources: The company can survey 400 customers.
 Calculation:
 Using standard formulas, the company determines that a sample size of 352 is needed.
However, to ensure a robust representation, they decide to survey 400 customers.
Sample size Selection :
Demographically and Geographically:
 Demographic Factors:
 Age: If the research aims to understand attitudes or behaviors across different age groups,
the sample should include a proportionate representation of each age category.
 Gender: If gender differences are of interest, the sample needs to include sufficient
numbers of both males and females.
 Income: Income levels may impact purchasing behavior, so the sample should represent
various income brackets.
 Education: Educational backgrounds can influence opinions, so the sample should reflect
diverse educational levels.
Geographic Factors:

 Location: If the research pertains to regional preferences or differences, the sample

should cover various geographical locations.
 Urban/Rural: Different urban and rural settings may have distinct preferences, requiring
representation from both.
 Climate Zones: Climate can impact consumer preferences, so the sample should consider
individuals from different climate zones if relevant.
Ques 5 Determination of sample size formula using Krejcie and morgon table. (No
numericals only explanation with proper formula ?
Ans 5 There are three methods :
 1.Determination of sample size Krejcie and morgon table
The Krejcie and Morgan table is a resource commonly used in research to determine the
appropriate sample size for a survey when dealing with a finite population. This method is
particularly useful when you want to ensure that your sample is representative of the entire
population and when you are conducting a simple random sampling technique.
Formula : n=x2 Np(1-p) Pls Check Formula from NB
E2 (N-1)+X2 p)1-p) Here the E is in small letter and X also in small
letter
n : Sample size S = n ( Both sample size )
N : Population Size
e : Acceptable sampling error
X2 : Chi-Square of degree of freedom 1 and confidence level 95 %
= 3.841

 2.Standard sample size formula (Cochran formula) when there is Z value use cochran
formula
The Cochran formula, named after William G. Cochran, is a standard method used to determine
the sample size in a survey or experiment. This formula is commonly applied when dealing with
a large population, and the goal is to estimate a proportion or prevalence within that population.
The formula takes into account the desired confidence level, margin of error, and estimated
proportion of the characteristic of interest.
 To be used when population is infinite
 To be used when you do not know the population size (N).
Formula : S=Z2 X Check formula from nb

σ X (1- σ) / (E)2

S = sample size
Z = Confidence level
σ = Standard deviation
E = Margin of error
 1 Marginal error : The margin of error is considered to be the amount of error that can be
allowed in the study. The margin of error is actually a percentage that shows how close
the sample results will be with respect to the true value of the overall population that is
considered in the study.
2. Confidence error : The confidence error is pretty closely related to the margin of error
or confidence interval. This value is used to measure the degree of certainty about how
well a sample actually represents the entire population within the margin of error chosen
for the study.
3. Sample size calculations (Yamane’s Formula)
Yamane's Formula is a widely used method for determining the sample size in a research study,
particularly in the field of survey research. Developed by K. Yamane, this formula is applicable
when dealing with a large population where the exact size is known, and you want to ensure that
your sample is representative. The formula is expressed as:

 To be used when population is finite.

 To be used when you know the population size (N)
Formula :

Ques 6 What are the types of sampling ? Techniques and methods ?

Ans 6 Probability sampling and non probability sampling :
Probability sampling involves random selection, allowing you to make strong statistical
inferences about the whole group. Example : Blood donation camp is all for everyone , first
come first service.
Non-probability sampling involves non-random selection based on convenience or other criteria,
allowing you to easily collect data. Example : Invited only specific student for blood donation
camp.
Probability sampling types with example : Technique/method
1 1. Simple random sampling
In a simple random sample, every member of the population has an equal chance of being
selected. Your sampling frame should include the whole population.
To conduct this type of sampling, you can use tools like random number generators or other
techniques that are based entirely on chance

 Example : Simple random sampling

 You want to select a simple random sample of 1000 employees of a social media
marketing company. You assign a number to every employee in the company database
from 1 to 1000, and use a random number generator to select 100 numbers.
2 Stratified sampling
Stratified sampling involves dividing the population into subpopulations that may differ in
important ways. It allows you draw more precise conclusions by ensuring that every subgroup is
properly represented in the sample.
To use this sampling method, you divide the population into subgroups (called strata) based on
the relevant characteristic (e.g., gender identity, age range, income bracket, job role).

 Example : Dividing the group on the basis of income , interest , employment for
purchasing the audi car.
 Example : The company has 800 female employees and 200 male employees. You want
to ensure that the sample reflects the gender balance of the company, so you sort the
population into two strata based on gender. Then you use random sampling on each
group, selecting 80 women and 20 men, which gives you a representative sample of 100
people.
3. Systematic sampling
Systematic sampling is similar to simple random sampling, but it is usually slightly easier to
conduct. Every member of the population is listed with a number, but instead of randomly
generating numbers, individuals are chosen at regular intervals.

 Example: Systematic sampling

 All employees of the company are listed in alphabetical order. From the first 10 numbers,
you randomly select a starting point: number 6. From number 6 onwards, every 10th
person on the list is selected (6, 16, 26, 36, and so on), and you end up with a sample of
100 people.
 Example : I am living a gap purposely. 11 th + 15 th = Gap of 5 (Formula : n + k (
Interval value)
4.Cluster sampling
Cluster sampling also involves dividing the population into subgroups, but each subgroup should
have similar characteristics to the whole sample. Instead of sampling individuals from each
subgroup, you randomly select entire subgroups.
  Example : In group there are 20 members , and Randomly I will pick one group to donate
the blood.
Example: Cluster sampling
 The company has offices in 10 cities across the country (all with roughly the same
number of employees in similar roles). You don’t have the capacity to travel to every
office to collect your data, so you use random sampling to select 3 offices – these are
your clusters.
5 Multistage Sampling:
Multistage sampling is a complex sampling technique that involves multiple stages of sampling.
It is often used when it is impractical or too costly to survey an entire population directly.
Instead, the population is divided into stages, and samples are taken from each stage. This
method allows for more manageable and cost-effective data collection.
Example : User of content and non- user content

One applied simple one applied systematic sampling

Ramdon sampling
Ques 7 What are the types of non sampling probability with example ?
Ans 7 1. Convenience sampling
A convenience sample simply includes the individuals who happen to be most accessible to the
researcher.This is an easy and inexpensive way to gather initial data, but there is no way to tell if
the sample is representative of the population, so it can’t produce generalizable results.
Convenience samples are at risk for both sampling bias and selection bias.
Example: Convenience sampling
You are researching opinions about student support services in your university, so after each of
your classes, you ask your fellow students to complete a survey on the topic. This is a convenient
way to gather data, but as you only surveyed students taking the same classes as you at the same
level, the sample is not representative of all the students at your university
2. . Purposive sampling
This type of sampling, also known as judgement sampling, involves the researcher using their
expertise to select a sample that is most useful to the purposes of the research.
Example: Purposive sampling
You want to know more about the opinions and experiences of disabled students at your
university, so you purposefully select a number of students with different support needs in order
to gather a varied range of data on their experiences with student services.
3.Referral/ Snowball Sampling:
Snowball sampling is a non-probability sampling method where existing study participants
recruit additional participants. This approach is useful when the population is hard to reach or
identify directly.
Example:
In a study on rare medical conditions, snowball sampling is used as the initial participants refer
others with similar conditions, creating a network for data collection. This method leverages
existing connections to access a difficult-to-reach population.
4. Quota Sampling:
Quota sampling is a non-probability sampling method where researchers establish predetermined
quotas for certain characteristics (e.g., age, gender) and then sample individuals who meet these
criteria until the quotas are filled.
Example:
In a market research survey, quota sampling is applied by setting quotas for age groups and
selecting participants until each age category is adequately represented. This method ensures a
proportional sample composition without random selection from the entire population.

Ques 8 What is sampling and the charactersistics of sampling technique ?

Ans 8 Sampling:
Sampling is the process of selecting a subset of elements from a larger population to study and
draw conclusions about that population. The goal is to obtain a representative group that
accurately reflects the characteristics of the entire population. Sampling is a practical and
efficient way to conduct research, especially when studying large or diverse populations.
Cost and Time Efficiency:
Sampling aims to achieve representative results while minimizing costs and time compared to
studying the entire population.
Reliability:
A good sampling technique produces reliable and consistent results, ensuring that the sample
accurately reflects the population.
In-Depth Study:
Sampling allows for a detailed examination of a subset of the population, facilitating a deeper
understanding of specific characteristics.
Scientific Approach:Sampling involves a systematic and scientific method of selecting
participants, ensuring objectivity and minimizing biases in the research process.
Suitability:
The sampling technique should be appropriate for the research objectives, population
characteristics, and the type of study being conducted. It must align with the study's goals.
These characteristics collectively contribute to the effectiveness and validity of the sampling
technique in producing meaningful and generalizable results from a subset of the population.

Ques 9 What is sampling distribution ? Explain the types of distributions ,sampling distribution
of mean , sampling distribution of proportion and T- Distribution with example ?
Ans 9 Sampling Distribution:
Sampling distribution is a statistic that determines the probability of an event based on data from
a small group within a large population. Its primary purpose is to establish representative results
of small samples of a comparatively larger population.
There are three standard types of sampling distributions in statistics:
1. Sampling distribution of mean
The most common type of sampling distribution is the mean. It focuses on calculating the mean
of every sample group chosen from the population and plotting the data points. The graph shows
a normal distribution where the center is the mean of the sampling distribution, which represents
the mean of the entire population.
Example: If you repeatedly draw samples of 50 apples from an orchard and calculate the mean
weight of each sample, the distribution of these sample means forms a sampling distribution of
the mean.
2. Sampling distribution of proportion
This sampling distribution focuses on proportions in a population. You select samples and
calculate their proportions. The means of the sample proportions from each group represent the
proportion of the entire population.
Example: Suppose you want to estimate the proportion of defective items in a factory. If you
take several random samples of 100 items each, count the defective ones in each sample, and
create a distribution of these proportions, it represents the sampling distribution of the
proportion.

 Used to : Estimate The Mean Of The Population ,

 Estimate The Standard Deviation ,
 Estimate The Confidence Interval ,
 Sample Size N<30( T - Distribution),
 Sample Size N> 30 (Normal Distribution )
3. T-distribution
A T-distribution is a sampling distribution that involves a small population or one where you
don't know much about it. It is used to estimate the mean of the population and other statistics
such as confidence intervals, statistical differences and linear regression. The T-distribution uses
a t-score to evaluate data that wouldn't be appropriate for a normal distribution
The formula for t-score is:
t = [ x - μ ] / S / Nn )

In the formula, "x" is the sample mean and "μ" is the population mean and signifies standard
deviation . n is the size of the given sample.
Example: Consider a study on the heights of 20 students. If you don't know the population
standard deviation and wish to estimate the average height with a 95% confidence interval, you'd
use a t-distribution due to the small sample size.

Ques 10 What are the steps in sampling / Sampling design ? Explain each step with
example.?
Ans 10 The five steps to sampling/ sampling design are:
1. Identify the Population:
Explanation: Clearly define the entire group or population that you want to study. This is the
complete set of individuals, objects, or events that the research aims to investigate.
Example: If you are conducting a study on smartphone usage habits among teenagers in a city,
the population is all teenagers in that city.
2. Specify a Sampling Frame:
Explanation: A sampling frame is a list or representation of the elements in the population from
which the sample will be drawn. It should cover the entire population and be accessible for the
sampling process.
Example: For the smartphone study, a sampling frame could be a list of high schools in the city,
as it includes the potential participants.
3. Specify a Sampling Method:
Explanation: Choose a method for selecting individuals from the sampling frame. Common
methods include random sampling, stratified sampling, cluster sampling, or convenience
sampling.Example: If you use random sampling, you might assign each teenager in the sampling
frame a number and randomly select a certain number of individuals for the study.
4. Determine the Sample Size:
Explanation: Decide how many individuals will be included in the sample. The sample size is
crucial for the reliability and generalizability of the study.
Example: If you determine that a sample size of 200 teenagers is sufficient for your smartphone
study, this is the number you would aim to include in your research.
5. Implement the Plan:
Explanation: Execute the sampling plan by actually selecting the individuals from the sampling
frame according to the specified sampling method and sample size.
Example: Following the plan, randomly select 200 teenagers from the list of high schools in the
city to participate in your smartphone usage study.
These steps ensure a systematic and representative selection process, enhancing the validity and
reliability of the study's findings.

Cover everything as per nb and handbook