### 统计代写|生物统计代写biostatistics代考| RANDOM SAMPLING

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|生物统计代写biostatistics代考|OBTAINING REPRESENTATIVE DATA

The purpose of sampling is to get a sufficient amount of data that is representative of target population so that statistical inferences can be made about the distribution and the parameters of the target population. Because a sample is only a subset of the units in the target population, it is generally impossible to guarantee that the sample data are representative of the target population; however, with a well-designed sampling plan, it will be unlikely to select a sample that is not representative of the target population. To ensure the likelihood that the sample data will be representative of the target population, the following components of the sampling process must be considered:

• Target Population The target population must be well defined, accessible, and the researcher should have a good understanding of the structure of the population. In particular, the researcher should be able to identify the units of the population, the approximate number of units in the population, subpopulations, the approximate shape of the distributions of the variables being studied, and the relevant parameters that need to be estimated.
• Sampling Units The Sampling units are the units of the population that will be sampled. A sampling unit may or may not be a unit of the population. In fact, in some sampling plans, the sampling unit is a collection of population units. The sampling unit is also the smallest unit in the target population that can be selected.
• Sampling Element A sampling element is an object on which measurements will be made. A sampling element may or may not be a sampling unit. When the sampling unit consists of several population units, it is called a cluster of units. If each

population unit in a cluster will be measured, then the sampling elements are the population units within the sampled clusters. In this case, the sampling element is a subunit of the sampling unit.

• Sampling Frame The sampling frame is the list of sampling units that are available for sampling. The sampling frame should be nearly equal to the target population. When the sampling frame is significantly different from the target population, it makes it less unlikely that a sample representative of the target population will be obtained, even with a well-designed sampling plan. Sampling frames that fail to include all of the units of the target population are said to undercover the target population and may lead to biased samples.
• Sample Size The sample size is the number of sampling units that will be selected. The sample size will be denoted by $n$ and must be sufficiently large to ensure the reliability of the statistical analysis. The variability in the target population plays a key role in determining the sample size necessary for the desired level of reliability associated with a statistical analysis.

## 统计代写|生物统计代写biostatistics代考|Probability Samples

The statistical theory that provides the foundation for the estimation or testing of research hypotheses about the parameters of a population is based on the sampling structure known as probability sampling. A probability sample is a sample that is selected in a random fashion according to some probability model. In particular, a probability sample is a sample chosen so that each of the possible samples is known in advance and the probability of drawing each sampling unit is known. Random samples are samples that arise through a sampling plan based on probability sampling.

Probability sampling allows flexibility in the sampling plan and can be designed specifically for the target population being studied. That is, a probability sampling plan allows a sample to be designed so that it will be unlikely to produce a sample that is not representative of the target population. Furthermore, probability samples allow for confidence statements and hypothesis tests to be made from the observed sample with a high degree of reliability.

Samples of convenience are samples that are not based on probability samples and are also referred to as nonprobability samples. The statistical theory that justifies the use of confidence statements and tests of hypotheses does not apply to nonprobability samples; therefore, confidence statements and test of the research hypotheses based on nonprobability samples are erroneous applications of statistics and should not be trusted.
In a random sample, the chance that a particular unit of the population will be selected is known prior to sampling, and the units available for sampling are selected at random according to these probabilities. The procedure for drawing a random sample is outlined below.

## 统计代写|生物统计代写biostatistics代考|Simple Random Sampling

The first sampling plan that will be discussed is the simple random sample. A simple random sample of size $n$ is a sample consisting of $n$ sampling units selected in a fashion that every possible sample of $n$ units has the same chance of being selected. In a simple random sample, every possible sample has the same chance of being selected, and moreover, each sampling unit has the same chance of being drawn in a sample. Simple random sampling is a reasonable sampling plan for sampling homogeneous or heterogeneous populations that do not have distinct subpopulations that are of interest to the researcher.
Example 3.3
Simple random sampling might be a reasonable sampling plan in the following scenarios:
a. A pharmaceutical company is checking the quality control issues of the tablet form of a new drug. Here, the company might take a random sample of tablets from a large pool of available drug tablets it has recently manufactured.
b. The Federal Food and Drug Administration (FDA) may take a simple random sample of a particular food product to check the validity of the information on the nutrition label.
c. A state might wish to take a simple random sample of medical doctors to review whether or not the state’s continuing education requirements are being satisfied.
d. A federal or state environment agency may wish to take a simple random sample of homes in a mining town to investigate the general health of the town’s inhabitants and contamination problems in the homes resulting from the mining operation.

The number of possible simple random samples of size $n$ selected from a sampling frame listing of $N$ sampling units is
$$\left(\begin{array}{l} N \ n \end{array}\right)=\frac{N !}{n !(N-n) !}$$
The probability that any one of the possible simple random samples of $n$ units selected from a sampling frame of $N$ units is
$$\frac{1}{\frac{N !}{n !(N-n) !}}=\frac{n !(N-n) !}{N !}$$

## 统计代写|生物统计代写biostatistics代考|OBTAINING REPRESENTATIVE DATA

• 目标人群 目标人群必须明确定义、易于访问，并且研究人员应对人群结构有很好的了解。特别是，研究人员应该能够识别总体单位、总体中单位的大致数量、亚总体、所研究变量分布的大致形状以及需要估计的相关参数。
• 抽样单位 抽样单位是要抽样的总体单位。抽样单位可能是也可能不是人口的单位。事实上，在一些抽样计划中，抽样单位是人口单位的集合。抽样单位也是目标人群中可以选择的最小单位。
• 采样元件 采样元件是将对其进行测量的对象。采样元件可以是也可以不是采样单元。当抽样单位由若干人口单位组成时，称为单位群。如果每个

• 抽样框架 抽样框架是可用于抽样的抽样单位列表。抽样框架应该几乎等于目标人群。当抽样框架与目标人群显着不同时，即使采用精心设计的抽样计划，也不太可能获得代表目标人群的样本。未能包括目标总体的所有单位的抽样框架被称为隐藏目标总体，并可能导致样本有偏差。
• 样本大小 样本大小是要选择的抽样单位的数量。样本大小将表示为n并且必须足够大以确保统计分析的可靠性。目标人群的可变性在确定与统计分析相关的所需可靠性水平所需的样本量方面起着关键作用。

## 统计代写|生物统计代写biostatistics代考|Simple Random Sampling

：一家制药公司正在检查一种新药片剂的质量控制问题。在这里，该公司可能会从其最近生产的大量可用药片中随机抽取片剂样本。

C。一个州可能希望对医生进行简单的随机抽样，以审查该州的继续教育要求是否得到满足。
d。联邦或州环境机构可能希望对采矿城镇中的房屋进行简单的随机抽样，以调查该镇居民的总体健康状况以及采矿作业导致的房屋污染问题。

(ñ n)=ñ!n!(ñ−n)!

1ñ!n!(ñ−n)!=n!(ñ−n)!ñ!

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。