## 统计代写|假设检验代写hypothesis testing代考|MA121

2022年10月17日

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## 统计代写|假设检验代写hypothesis testing代考|What is Binomial distribution

A single experiment with two outcomes can be described by Bernoulli distribution. Suppose there are $n$ trials (experiments) with only two outcomes each, this experiment is called a binomial experiment, and the distribution that describes a binomial experiment is called binomial distribution.
Each binomial experiment should satisfy the following properties:

1. There are $n$ trials (experiments), each with two outcomes: success and failure.
2. The trials are independent.
3. The probability of success remains constant for all experiments.

Suppose there is a binomial experiment consisting of $n$ experiments, then the probability distribution for binomial variable $Y$ is called binomial distribution having the mathematical formula presented in Eq. (4.2).
$$P(Y)=C_Y^n p^Y q^{n-Y} \quad Y=1,2, \ldots, n$$
$Y \sim b(Y, n, p)$ represents a variable $Y$ that follows binomial distribution with probability $p$ where, $Y$ represents the number of successes obtained from a binomial experiment. $n$ represents the total number of experiments in a binomial experiment. $p$ represents the probability of success for each experiment. $q$ represents the probability of failure for the experiment, $(q=1-p)$. $P(Y)$ represents the probability of obtaining exactly $Y$ successes.
The mean and variance of binomial distribution are:
\begin{aligned} &\mu=n p \ &\sigma^2=n p q \end{aligned}
A graphical presentation for binomial distribution is given in Fig. 4.1.

## 统计代写|假设检验代写hypothesis testing代考|Hypothesis testing for one sample proportion

Hypothesis testing for proportion needs to know the concept of proportion, how to calculate the proportion, and other related concepts and terms. As an example for the proportion, we might wish to know the proportion of landfills that show a specific bacteria among 20 landfills. Suppose that only four out of 20 landfills have this type of bacteria, thus, $\frac{4}{20}=\frac{1}{5}=0.20$ or $20 \%$. The value of $20 \%$ represents the proportion of landfills that have a specific bacteria.

Proportion $(\hat{p})$ is a value calculated from the sample data to show the percentage of a part that carry a certain attribute to the whole. The formula for computing the proportion is given in Eq. (4.3).
$$\hat{p}=\frac{Y}{n}$$
where $Y$ is the number of observations in the selected sample that carry the certain attribute, and $n$ is the sample size.

The concept of proportion belongs to the family of experiments of two outcomes which follow binomial distribution. If the sample size is large and the probability of success $P$ is small, such that $n p \geq 5$ and $n q \geq 5$, then binomial distribution can be approximated by the normal distribution.

Consider a large sample that is selected from a normally distributed population and $Y$ represents a random variable of interest. A claim regarding the proportion value of the variable of interest can be tested employing Z-test for one sample proportion to make a decision regarding the hypothesis of the proportion value. The mathematical formula for computing the test statistic value for one sample proportion employing Z-test is presented in Eq. (4.4).
$$Z=\frac{\hat{p}-p}{\sqrt{p q / n}}$$
where $\mathrm{Z}$ is the test statistic, $p$ is the claimed proportion (hypothesized proportion), and $\hat{p}$ is the sample proportion which is calculated as:
$$\hat{p}=\frac{Y}{n}$$
where $Y$ is the number of individuals (units) in the sample that possess the characteristic of interest, and $q=\frac{n-Y}{n}$ or $1-p$, and $n$ is the sample size.

# 假设检验代写

## 统计代写|假设检验代写假设检验代考|什么是二项分布

• 试验是独立的。
• 所有实验的成功概率保持不变

Suppose there is a binomial experiment consisting of $n$ 实验，然后给出二项变量的概率分布 $Y$ 称为二项分布，其数学公式如式(4.2)所示。
$$P(Y)=C_Y^n p^Y q^{n-Y} \quad Y=1,2, \ldots, n$$
$Y \sim b(Y, n, p)$ 表示一个变量 $Y$ 它遵循概率二项分布 $p$ 其中， $Y$ 表示从二项实验中获得的成功数。 $n$ 表示二项实验的实验总数。 $p$ 表示每个实验成功的概率。 $q$ 表示实验失败的概率， $(q=1-p)$。 $P(Y)$ 表示精确获得的概率 $Y$ 成功。二项分布的均值和方差分别为:
\begin{aligned} &\mu=n p \ &\sigma^2=n p q \end{aligned}图4.1给出了二项分布的图形表示

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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。