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Related Concept Videos

Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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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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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.
The confidence interval estimate will have the form as follows:
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What are Estimates?01:06

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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. 
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Distributions to Estimate Population Parameter01:26

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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...
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Estimating Population Standard Deviation01:26

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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...
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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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A generalized exponential-type estimator for population mean using auxiliary attributes.

Sohail Ahmad1, Muhammad Arslan2, Aamna Khan3

  • 1Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan.

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|May 13, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces new exponential estimators for finite population mean estimation using auxiliary attributes. These novel estimators demonstrate superior performance in both simple and stratified random sampling methods.

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Accurate estimation of finite population parameters is crucial in statistical analysis.
  • Existing estimators may have limitations in efficiency when using auxiliary information.
  • The use of auxiliary attributes can improve the precision of survey estimates.

Purpose of the Study:

  • To propose a generalized class of exponential type estimators for finite population mean.
  • To evaluate the performance of these estimators under simple random sampling and stratified random sampling.
  • To compare the proposed estimators with existing ones using theoretical and empirical methods.

Main Methods:

  • Development of a generalized class of exponential type estimators.
  • Derivation of bias and mean squared error (MSE) up to the first order of approximation.
  • Empirical evaluation using four real-world populations.

Main Results:

  • The proposed class of estimators showed improved performance compared to existing estimators.
  • Theoretical derivations provided a basis for the observed performance gains.
  • Empirical results consistently supported the superiority of the proposed estimators.

Conclusions:

  • The generalized exponential type estimators offer a more efficient approach for finite population mean estimation.
  • The proposed method is effective under both simple random sampling and stratified random sampling designs.
  • This research contributes to the advancement of estimation techniques in survey statistics.