This document discusses sampling and estimation. It defines a population as the complete set of elements sharing a common characteristic, while a sample is a subset of the population that is representative of it. Random sampling is described as selecting samples in a way that gives each member of the population an equal chance of being chosen, resulting in an unbiased representation. Sampling error occurs when using a sample rather than the entire population, as the sample statistic may differ from the true population parameter. Larger sample sizes reduce sampling error, while non-sampling errors from issues like biases cannot be addressed this way.

1. SAMPLING AND
ESTIMATION

2. OBJECTIVES
• Understand the distinction between a sample and population.
• Elementary understanding of the use of random variables in producing
random samples.
• Recognize that a sample mean can be regarded as a random variable, and use
the facts that E(X)= µ and that Var(X)=σ

3. What is the ‘population’ ?
• Definition: Population in research is a complete set of elements that possess
a standard parameter between them.
• We are all aware of what the word ‘population’ means in our everyday life.
Frequently it is used to describe the human population or the total number
of people living in a geographic area of our country or state.
• The ‘population’ in research doesn’t necessarily have to be human. It can be
any parameter of data that possesses a common trait.

4. What is a sample ?
• Definition: A sample is a smaller part of the whole, i.e., a subset of the
entire population. It is representative of the population in a study. When
conducting surveys, the sample is the members of the population who are
invited to participate in the survey. Hence said, a sample is a subgroup or
subset within the population. This sample can be studied to investigate the
characteristics or behavior of the entire population data.

5. WHAT IS RandomSampling?
• Definition: Random sampling is a part of
the sampling technique in which each sample
has an equal probability of being chosen. A
sample chosen randomly is meant to be an
unbiased representation of the total
population. If for some reasons, the sample
does not represent the population, the
variation is called a sampling error.

6. What is Sampling Error?
• Errors happen when you take a sample from the population rather than
using the entire population. In other words, it’s the difference between
the statistic you measure and the parameter you would find if you took
a census of the entire population.
• If you were to survey the entire population (like the US Census), there would
be no error. It’s nearly impossible to calculate the error margin. However,
when you take samples at random, you estimate the error and call it
the margin of error.

7. • Sample error can only be reduced, this is because it is considered to be an
acceptable tradeoff to avoid measuring the entire population. In general, the
larger the sample, the smaller the margin of error. There is a notable
exception: if you use cluster sampling, this may increase the error because of
the similarities between cluster members. A carefully designed experiment or
survey can also reduce error.

8. Another Type of Error
• The non-sampling error could be one reason as to why there’s a difference
between the sample and the population. This is due to poor data collection
methods (like faulty instruments or inaccurate data recording), selection
bias, non response bias (where individuals don’t want to or can’t respond to a
survey), or other mistakes in collecting the data. Increasing the sample size
will not reduce these errors. They key is to avoid making the errors in the
first place with a well-planned design for the survey or experiment.