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Related Concept Videos

Sampling Distribution01:12

Sampling Distribution

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Testing a Claim about Mean: Known Population SD01:11

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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...
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Testing a Claim about Mean: Unknown Population SD01:21

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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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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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Confidence Interval for Estimating Population Mean01:25

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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.
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Estimating Population Mean with Known Standard Deviation01:16

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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.
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Acceptance Probabilities for a Sampling Procedure Based on the Mean and an Order Statistic.

Mary C Croarkin1, Grace L Yang1

  • 1Nationol Bureau of Standards, Washington, DC 20234.

Journal of Research of the National Bureau of Standards (1977)
|September 27, 2021
PubMed
Summary

This study investigates a dual acceptance criterion for inspection, developing an approximation and lower bound for acceptance probability applicable to continuous distributions. The findings connect this criterion to hypothesis testing, providing exact power calculations for exponential distributions.

Keywords:
acceptance probabilitycompliance samplingdual acceptance criteriamixed sampling planorder statisticsstatistical methods

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Area of Science:

  • Statistical Quality Control
  • Probability Theory

Background:

  • Inspection procedures often employ dual acceptance criteria combining sample means with extreme order statistics.
  • Accurate computation of acceptance probabilities for these criteria is essential for reliable quality assessment.

Purpose of the Study:

  • To investigate the computation of acceptance probability for dual acceptance criteria.
  • To develop approximations and lower bounds for this probability.
  • To explore the link between dual criteria and hypothesis testing.

Main Methods:

  • Derivation of an approximation and a lower bound for acceptance probability.
  • Analysis of the relationship between the dual criterion and hypothesis testing for scale and location parameters.
  • Exact evaluation of acceptance probability for the exponential distribution.

Main Results:

  • An approximation and a lower bound for acceptance probability were derived, applicable to any continuous distribution.
  • The study established a connection between the dual acceptance criterion and hypothesis testing.
  • For exponential distributions, the exact acceptance probability calculation determined the test power.

Conclusions:

  • The developed methods provide valuable tools for analyzing dual acceptance criteria in statistical inspection.
  • The findings enhance understanding of the relationship between acceptance sampling and hypothesis testing.
  • The research offers precise power calculations for hypothesis tests involving exponential distributions.