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Confidence Interval for Estimating Population Mean

Confidence Interval for Estimating Population Mean

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...

Interpretation of Confidence Intervals

Interpretation of Confidence Intervals

A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...

Estimating Population Standard Deviation

Estimating Population Standard Deviation

When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...

Distributions to Estimate Population Parameter

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...

Bias

Bias

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The Representativeness Heuristic

The Representativeness Heuristic

The representative heuristic describes a biased way of thinking, in which you unintentionally stereotype someone or something. For example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

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Related Experiment Video

Updated: May 28, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Statistical judgments are influenced by the implied likelihood that samples represent the same population.

Dana L Chesney¹, Natalie A Obrecht

¹Department of Psychology, University of Notre Dame, 118 Haggar Hall, Notre Dame, IN 46556, USA. Dana.Chesney.3@nd.edu

Memory & Cognition

|October 29, 2011

Summary

Laypeople

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Published on: September 11, 2021

Area of Science:

Cognitive Psychology
Decision Making
Statistical Reasoning

Background:

Normative statistical practice weights information by sample size.
Combining estimates from different subpopulations may not require sample size weighting.
Laypeople's statistical judgment heuristics are not fully understood.

Purpose of the Study:

To investigate if laypeople consider population likelihood when combining sample information.
To determine how implied sampling processes influence statistical judgments.
To examine the role of numeracy in normative statistical reasoning.

Main Methods:

Two experiments were conducted to assess laypeople's judgments.
Participants evaluated sample information under different implied sampling conditions.
Statistical judgments were correlated with individual numeracy levels.

Main Results:

Implied variability influenced judgments of sample origin likelihood.
Sample size had a greater impact when samples were from a general population versus subpopulations.
Higher numeracy correlated with more normative weighting of sample information.

Conclusions:

Laypeople integrate likelihood and sampling process information into statistical judgments.
Heuristics used by laypeople deviate from normative statistical weighting under certain conditions.
Understanding these cognitive processes is crucial for statistical education and debiasing efforts.