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Related Concept Videos

Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

8.6K
In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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What are Estimates?01:06

What are Estimates?

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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such...
7.6K
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

8.5K
A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
8.5K
Testing a Claim about Mean: Known Population SD01:11

Testing a Claim about Mean: Known Population SD

3.0K
A complete procedure of testing the hypothesis about a population mean is explained here.
Estimating a population mean requires the samples to be distributed normally. The data should be collected from the randomly selected samples having no sampling bias. The sample size needed to be higher than 30, and most importantly, the population standard deviation should be already known.
In most realistic situations, the population standard deviation is often unknown, but in rare circumstances, when it...
3.0K
Testing a Claim about Mean: Unknown Population SD01:21

Testing a Claim about Mean: Unknown Population SD

5.1K
A complete procedure of testing a hypothesis about a population mean when the population standard deviation is unknown is explained here.
Estimating a population mean requires the samples to be approximately normally distributed. The data should be collected from the randomly selected samples having no sampling bias. There is no specific requirement for sample size. But if the sample size is less than 30, and we don't know the population standard deviation, a different approach is used;...
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Updated: Nov 27, 2025

Integrating Computerized Linguistic and Social Network Analyses to Capture Addiction Recovery Capital in an Online Community
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Inferring the Population Mean with Second-Order Information in Online Social Networks.

Saran Chen1, Xin Lu1,2,3,4, Zhong Liu1

  • 1College of Systems Engineering, National University of Defense Technology, Changsha 410073, China.

Entropy (Basel, Switzerland)
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Summary

This study introduces a novel online survey method that asks respondents about their friends

Keywords:
online surveyspopulation mean inferencesecond-order informationsensitive variable

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Area of Science:

  • Social Sciences
  • Statistics
  • Computer Science

Background:

  • Online surveys are prevalent in public health, business, and sociology for data collection.
  • Self-reported data in online surveys face challenges like low response rates and unreliability, especially for sensitive topics.
  • Existing methods struggle with privacy concerns and data accuracy for sensitive variables.

Purpose of the Study:

  • To develop an alternative online survey approach to improve data reliability for sensitive questions.
  • To overcome limitations of direct self-reporting by collecting second-order information (friends' characteristics).
  • To enable accurate population inference without directly asking respondents sensitive personal questions.

Main Methods:

  • Developed a novel survey method collecting second-order information about respondents' social network connections.
  • Applied the Hansen-Hurwitz estimator for population inference using simple random sampling and random walk-based sampling.
  • Evaluated the approach through simulations on artificial and real-world network data.

Main Results:

  • The proposed method accurately estimates population variables without requiring respondents' direct self-disclosure.
  • Simulation results demonstrate high accuracy in population estimates across various network settings.
  • Biases in estimates were found to be small and within acceptable statistical limits.

Conclusions:

  • This novel approach offers a viable alternative for online survey implementation, enhancing data reliability.
  • It provides a method for improved population inference on sensitive variables by leveraging social network data.
  • The technique is expected to increase the quality of collected data in sensitive research areas.