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Confidence Intervals01:21

Confidence Intervals

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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...
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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

4.3K
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...
4.3K
Margin of Error01:27

Margin of Error

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The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.
4.5K
Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

6.5K
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...
6.5K
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

8.0K
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...
8.0K
Confidence Coefficient01:24

Confidence Coefficient

7.8K
The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
7.8K

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Related Experiment Video

Updated: Sep 8, 2025

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

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Confidence limits for conformance proportions in normal mixture models.

Shin-Fu Tsai1, Tse-Le Huang1

  • 1Department of Agronomy, National Taiwan University, Taipei, Taiwan.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for estimating conformance proportions in normal mixture models, crucial for quality assessments. The approach provides reliable confidence limits for both overall and specific population groups.

Keywords:
Generalized fiducial inferenceMarkov chain Monte Carlointerval estimationlatent variablequality control

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Area of Science:

  • Statistics
  • Quality Control
  • Data Analysis

Background:

  • Conformance proportions are key metrics for quality assessment.
  • Estimating these proportions is challenging within normal mixture models.

Purpose of the Study:

  • Define universal and individual conformance proportions for normal mixture models.
  • Develop a method to calculate confidence limits for these proportions.

Main Methods:

  • Utilized generalized fiducial quantities to establish a systematic estimation procedure.
  • Defined universal conformance proportions for overall population evaluation.
  • Defined individual conformance proportions for specific subpopulation assessment.

Main Results:

  • The proposed method effectively calculates confidence limits for conformance proportions.
  • Simulation results confirmed that the method maintains empirical coverage rates near nominal levels.
  • The approach is applicable to both overall and specific subpopulations.

Conclusions:

  • The generalized fiducial quantity-based method offers a robust way to estimate conformance proportions in normal mixture models.
  • This method is valuable for quality assessment and understanding population variations.
  • The approach demonstrated practical utility through illustrative examples.