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相关概念视频

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

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 +...
8.3K
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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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...
3.0K
One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

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One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
3.2K
What are Estimates?01:06

What are Estimates?

4.9K
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...
4.9K
Stratified Sampling Method01:16

Stratified Sampling Method

11.7K
Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a stratified sample, divide the population into groups called strata and then take a...
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相关实验视频

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Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits
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使用基于EWMA统计数据的内存类型估计器进行差异估计,用于分层采样中的时间尺度调查.

Muhammad Umair Tariq1, Muhammad Nouman Qureshi2, Osama Abdulaziz Alamri3

  • 1Department of Statistics, National College of Business Administration and Economics, Lahore, Pakistan.

Scientific reports
|November 4, 2024
PubMed
概括

新的记忆类型估计器通过使用过去的数据来改善分层采样中的人口变异估计. 与传统方法相比,这些增强方法在时间尺度调查中提供了更高的准确性.

关键词:
电子商务管理协会的统计数据辅助信息 辅助信息 辅助信息平均平方 错误 平均平方 错误记忆类型估计器分层分层是指分层的分层.时间尺度调查时间尺度调查.

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科学领域:

  • 统计 统计 统计 统计
  • 调查方法 调查方法

背景情况:

  • 在分层采样中的传统差异估计器可以通过整合历史数据来改进.
  • 现有的方法可能无法充分利用调查中的时间信息.

研究的目的:

  • 提出新的记忆类型指数和非指数估计器,用于分层采样中的人口变异.
  • 评估这些新估计器的表现和条件,这些新估计器的表现优于传统的估计器.

主要方法:

  • 使用泰勒和指数扩展来开发平均平方误差的数学表达式.
  • 导出内存类型估计器优越性的条件.
  • 在各种人口参数上进行了广泛的模拟研究.
  • 对现实世界数据集的应用.

主要成果:

  • 记忆类型估计器在分层采样中表现优于传统估计器,特别是在使用之前的样本信息时.
  • 获得并验证了提高性能的数学条件.
  • 模拟证实了时间尺度调查的提高效率.
  • 实际数据的应用支持了拟议的估计器的实际实用性.

结论:

  • 结合以前的样本信息可以显著提高时间尺度调查中差异估计的准确性和可靠性.
  • 拟议的内存类型估计器为分层采样中的统计分析提供了宝贵的进步.
  • 这些发现凸显了时间数据在调查方法中的整合的重要性.