PPT - Sampling Theory - 3

# PPT - Sampling Theory - 3 - Business Mathematics and Logical Reasoning & Statistics - CA Foundation

``` Page 1

CPT Section D Quantitative Aptitude Chapter 15
Prof. Bharat Koshti
Page 2

CPT Section D Quantitative Aptitude Chapter 15
Prof. Bharat Koshti
Theory of estimation :
It deals with estimating unknown values of the Population
parameters.
There are two types of estimation techniques :
1.Point Estimation
2. Interval Estimation
1. Point Estimation: When a single value is proposed to
estimate, it is called as Point estimation.
Page 3

CPT Section D Quantitative Aptitude Chapter 15
Prof. Bharat Koshti
Theory of estimation :
It deals with estimating unknown values of the Population
parameters.
There are two types of estimation techniques :
1.Point Estimation
2. Interval Estimation
1. Point Estimation: When a single value is proposed to
estimate, it is called as Point estimation.
1. Suppose the unknown parameter is ?.
(e.g. ? = Population Mean)
2. We take a sample of size ‘n’ from the population of
size ‘N’ at random. So we get sample observations
( x
1
, x
2
, x
3
,  ……………… x
n
)
3. Now based on these sample observations we
construct statistic T (e.g. Sample Mean) which will estimate ?
Page 4

CPT Section D Quantitative Aptitude Chapter 15
Prof. Bharat Koshti
Theory of estimation :
It deals with estimating unknown values of the Population
parameters.
There are two types of estimation techniques :
1.Point Estimation
2. Interval Estimation
1. Point Estimation: When a single value is proposed to
estimate, it is called as Point estimation.
1. Suppose the unknown parameter is ?.
(e.g. ? = Population Mean)
2. We take a sample of size ‘n’ from the population of
size ‘N’ at random. So we get sample observations
( x
1
, x
2
, x
3
,  ……………… x
n
)
3. Now based on these sample observations we
construct statistic T (e.g. Sample Mean) which will estimate ?
T is a single value obtained from the sample &
is known as point estimator.
The point estimator of Population Mean(µ),
Population Standard Deviation(s) & Population
Proportion(P) are the corresponding sample
Mean(x¯),Sample Standard Deviation(s) &
Sample Proportion(p).
Page 5

CPT Section D Quantitative Aptitude Chapter 15
Prof. Bharat Koshti
Theory of estimation :
It deals with estimating unknown values of the Population
parameters.
There are two types of estimation techniques :
1.Point Estimation
2. Interval Estimation
1. Point Estimation: When a single value is proposed to
estimate, it is called as Point estimation.
1. Suppose the unknown parameter is ?.
(e.g. ? = Population Mean)
2. We take a sample of size ‘n’ from the population of
size ‘N’ at random. So we get sample observations
( x
1
, x
2
, x
3
,  ……………… x
n
)
3. Now based on these sample observations we
construct statistic T (e.g. Sample Mean) which will estimate ?
T is a single value obtained from the sample &
is known as point estimator.
The point estimator of Population Mean(µ),
Population Standard Deviation(s) & Population
Proportion(P) are the corresponding sample
Mean(x¯),Sample Standard Deviation(s) &
Sample Proportion(p).
Ex1. Consider sample observations
14,15,6,17,28  from population of 100 units. Find
an estimate of population mean.
Estimate of µ is given by X¯
X¯ = (14+15+6+17+28)/5
X¯ = 16
Hence, estimate of µ is 16.
```

## Business Mathematics and Logical Reasoning & Statistics

128 videos|128 docs|87 tests

## FAQs on PPT - Sampling Theory - 3 - Business Mathematics and Logical Reasoning & Statistics - CA Foundation

 1. What is sampling theory and why is it important in statistics?
Sampling theory is a branch of statistics that deals with the selection and analysis of a subset of individuals or objects from a larger population. It is important because it allows us to make inferences about the entire population based on information collected from a smaller sample. By using sampling techniques, we can estimate population characteristics with a certain level of confidence, without having to study the entire population.
 2. What are the different types of sampling methods used in sampling theory?
There are several types of sampling methods used in sampling theory, including: 1. Simple Random Sampling: Every individual or object in the population has an equal chance of being selected. 2. Stratified Sampling: The population is divided into subgroups or strata, and then a random sample is taken from each stratum. 3. Cluster Sampling: The population is divided into clusters or groups, and then a random sample of clusters is selected for analysis. 4. Systematic Sampling: Individuals or objects are selected at regular intervals from a randomly chosen starting point. 5. Convenience Sampling: Individuals or objects are selected based on their easy accessibility or convenience.
 3. How does sample size affect the accuracy of statistical estimates in sampling theory?
Sample size plays a crucial role in the accuracy of statistical estimates in sampling theory. Generally, a larger sample size leads to more accurate estimates. This is because a larger sample size reduces the variability and sampling error, providing a more representative picture of the population. Smaller samples are more likely to produce estimates that deviate from the true population values, leading to less reliable results.
 4. What is sampling bias and how does it affect the validity of sampling theory?
Sampling bias refers to a systematic error in the sampling process that results in the over- or under-representation of certain individuals or objects in the sample. This bias can occur due to various reasons, such as non-random sampling methods or non-response from selected individuals. Sampling bias affects the validity of sampling theory by introducing a distortion in the estimates and making them unrepresentative of the population. It can lead to incorrect conclusions and poor decision-making based on the sample data.
 5. How can we minimize sampling error in sampling theory?
Sampling error is the difference between the sample estimate and the true population value. While it is impossible to completely eliminate sampling error, it can be minimized through various techniques: 1. Random Sampling: Using random sampling methods ensures that every individual or object in the population has an equal chance of being selected, reducing bias. 2. Increasing Sample Size: A larger sample size reduces variability and increases the precision of estimates, thereby decreasing sampling error. 3. Using Standardized Sampling Procedures: Following standardized procedures and protocols helps maintain consistency in the sampling process and reduces the chances of errors. 4. Conducting Pilot Studies: Pilot studies allow researchers to identify potential issues and refine the sampling process before collecting data on a larger scale. 5. Using Statistical Techniques: Employing appropriate statistical techniques can help correct for sampling errors and improve the accuracy of estimates.

## Business Mathematics and Logical Reasoning & Statistics

128 videos|128 docs|87 tests

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