## 统计代写|假设检验代写hypothesis testing代考|BSTA511

statistics-lab™ 为您的留学生涯保驾护航 在假设检验hypothesis testing作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在假设检验hypothesis testing代写方面经验极为丰富，各种假设检验hypothesis testing相关的作业也就用不着 说。

• 时间序列分析Time-Series Analysis
• 马尔科夫过程 Markov process
• 随机最优控制stochastic optimal control
• 粒子滤波 Particle Filter
• 采样理论 sampling theory

## 统计代写|假设检验代写hypothesis testing代考|Estimating the Standard Error of the Sample Quantile

Assuming that observations are randomly sampled from a continuous distribution, and that $f\left(x_q\right)>0$, the influence function of the qth quantile is
$$I F_q(x)= \begin{cases}\frac{q-1}{f\left(x_q\right)}, & \text { if } xx_q,\end{cases}$$
and
$$\hat{x}q=x_q+\frac{1}{n} \sum I F_q\left(X_i\right)$$ plus a remainder term that goes to zero as $n$ gets large. That is, the situation is similar to the trimmed mean in the sense that the estimate of the $q$ th quantile can be written as $x_q$, the population parameter being estimated, plus a sum of independent identically distributed random variables having a mean of zero, plus a term that can be ignored as the sample size gets large. Consequently, the influence function of the qth quantile can be used to determine the (asymptotic) standard error of $\hat{x}_q$. The result is $$V A R\left(\hat{x}_q\right)=\frac{q(1-q)}{n\left[f\left(x_q\right)\right]^2} .$$ For example, when estimating the median, $q=0.5$, and the variance of $\hat{x}{.5}$ is
$$\frac{1}{4 n\left[f\left(x_{.5}\right)\right]^2}$$
so the standard error of $\hat{x}{0.5}$ is $$\frac{1}{2 \sqrt{n} f\left(x{.5}\right)}$$
Moreover, for any $q$ between 0 and 1 ,
$$2 \sqrt{n} f\left(x_q\right)\left(\hat{x}_q-x_q\right)$$
approaches a standard normal distribution as $n$ goes to infinity.

## 统计代写|假设检验代写hypothesis testing代考|The Maritz–Jarrett Estimate of the Standard Error of x

Maritz and Jarrett (1978) derived an estimate of the standard error of sample median, which is easily extended to the more general case involving $\hat{x}_q$. That is, when using a single order statistic, its standard error can be estimated using the method outlined here. It is based on the fact that $E\left(\hat{x}_q\right)$ and $E\left(\hat{x}_q^2\right)$ can be related to a beta distribution. The beta probability density function, when $a$ and $b$ are positive integers, is
$$f(x)=\frac{(a+b+1) !}{a ! b !} x^a(1-x)^b, \quad 0 \leq x \leq 1 .$$
Details about the beta distribution are not important here. Interested readers can refer to Johnson and Kotz (1970, Chapter 24).

As before, let $m=[q n+0.5]$. Let $Y$ be a random variable having a beta distribution with $a=m-1$ and $b=n-m$, and let
$$W_i=P\left(\frac{i-1}{n} \leq Y \leq \frac{i}{n}\right) .$$
Many statistical computing packages have functions that evaluate the beta distribution, so evaluating the $W_i$ values is relatively easy to do. In $\mathrm{R}$, there is the function pbeta $(\mathrm{x}, \mathrm{a}, \mathrm{b})$ that computes $P(Y \leq x)$. Thus, $W_i$ can be computed by setting $x=i / n, y=(i-1) / n$, in which case $W_i$ is pbeta $(\mathrm{x}, \mathrm{m}-1, \mathrm{n}-\mathrm{m})$ minus pbeta $(\mathrm{y}, \mathrm{m}-1, \mathrm{n}-\mathrm{m})$.
Let
$$C_k=\sum_{i=1}^n W_i X_{(i)}^k$$
When $k=1, C_k$ is a linear combination of the order statistics. Linear sums of order statistics are called $L$-estimators. Other examples of L-estimators are the trimmed and Winsorized means already discussed. The point here is that $C_k$ can be shown to estimate $E\left(X_{(m)}^k\right)$, the $k$ th moment of the $m$ th order statistic. Consequently, the standard error of the $m$ th order statistic, $X_{(m)}=\hat{x}_q$, is estimated with
$$\sqrt{C_2-C_1^2}$$
Note that when $n$ is odd, this last equation provides an alternative to the McKean-Schrader estimate of the standard error of $M$ described in Section 3.3.4. Based on limited studies, it seems that when computing confidence intervals or testing hypotheses based on $M$, the McKean-Schrader estimator is preferable.

# 假设检验代写

## 统计代写|假设检验代写hypothesis testing代考|Estimating the Standard Error of the Sample Quantile

$$I F_q(x)=\left{\frac{q-1}{f\left(x_q\right)}, \quad \text { if } x x_q,\right.$$

$$\hat{x} q=x_q+\frac{1}{n} \sum I F_q\left(X_i\right)$$

$$\frac{1}{2 \sqrt{n} f(x .5)}$$

$$2 \sqrt{n} f\left(x_q\right)\left(\hat{x}_q-x_q\right)$$

## 统计代写|假设检验代写hypothesis testing代考|The Maritz–Jarrett Estimate of the Standard Error of x

Maritz 和Jarrett (1978) 得出了样本中位数标准误差的估计值，这很容易扩展到更一般的情况，涉及 $\hat{x}q$. 也就是说，当使用单阶统计量时，可以使用此处概述的方法估算其标准误差。这是基于这样一个事实 $E\left(\hat{x}_q\right)$ 和 $E\left(\hat{x}_q^2\right)$ 可能与 beta 分布有关。beta概率密度函数，当 $a$ 和 $b$ 是正整数，是 $$f(x)=\frac{(a+b+1) !}{a ! b !} x^a(1-x)^b, \quad 0 \leq x \leq 1$$ 关于 beta 分布的细节在这里并不重要。有兴趣的读者可以参考Johnson 和 Kotz（1970，第 24 章)。 和以前一样，让 $m=[q n+0.5]$. 让 $Y$ 是具有 beta 分布的随机变量 $a=m-1$ 和 $b=n-m$ ，然后让 $$W_i=P\left(\frac{i-1}{n} \leq Y \leq \frac{i}{n}\right) .$$ 许多统计计算包具有评估 beta 分布的函数，因此评估 $W_i$ 值是比较容易做到的。在 $\mathrm{R}$, 有函数 pbeta $(\mathrm{x}, \mathrm{a}, \mathrm{b})$ 计算 $P(Y \leq x)$. 因此， $W_i$ 可以通过设置计算 $x=i / n, y=(i-1) / n$ ，在这种情况下 $W_i$ 是 $\beta \beta(\mathrm{x}, \mathrm{m}-1, \mathrm{n}-\mathrm{m})$ 较少的 $\beta \beta(\mathrm{y}, \mathrm{m}-1, \mathrm{n}-\mathrm{m})$. 让 $$C_k=\sum{i=1}^n W_i X_{(i)}^k$$

$$\sqrt{C_2-C_1^2}$$

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国英国加拿大澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|假设检验代写hypothesis testing代考|STA2023

statistics-lab™ 为您的留学生涯保驾护航 在假设检验hypothesis testing作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在假设检验hypothesis testing代写方面经验极为丰富，各种假设检验hypothesis testing相关的作业也就用不着 说。

• 时间序列分析Time-Series Analysis
• 马尔科夫过程 Markov process
• 随机最优控制stochastic optimal control
• 粒子滤波 Particle Filter
• 采样理论 sampling theory

## 统计代写|假设检验代写hypothesis testing代考|The Finite Sample Breakdown Point

Before describing additional measures of location, it helps to introduce a technical device for judging any estimator that is being considered. This is the finite sample breakdown point of a statistic, which refers to the smallest proportion of observations that, when altered sufficiently, can render the statistic meaningless. More precisely, the finite sample breakdown point of an estimator refers to the smallest proportion of observations that when altered can cause the value of the statistic to be arbitrarily large or small. The finite sample breakdown point of an estimator is a measure of its resistance to contamination. For example, if the $i$ th observation among the observations $X_1, \ldots, X_n$ goes to infinity, the sample mean $\bar{X}$ goes to infinity as well. This means that the finite sample breakdown point of the sample mean is only $1 / n$. In contrast, the finite sample breakdown point of the $\gamma$-trimmed mean is $\gamma$. For example, if $\gamma=0.2$, about $20 \%$ of the observations can be made arbitrarily large without driving the sample trimmed mean to infinity, but it is possible to alter $21 \%$ of the observations so that $\bar{X}_t$ becomes arbitrarily large. Typically, the limiting value of the finite sample breakdown point is equal to the breakdown point, as defined in Chapter 2 , of the parameter being estimated. For example, the breakdown point of the population mean, $\mu$, is 0 , which equals $1 / n$ as $n$ goes to infinity. Similarly, the breakdown point of the trimmed mean is $\gamma$.

Two points should be stressed. First, having a high finite-sample breakdown point is certainly a step in the right direction when trying to deal with unusual values that have an inordinate influence, but it is no guarantee that an estimator will not be unduly influenced by even a small number of outliers. (Examples will be given when dealing with robust regression estimators.) Second, various refinements regarding the definition of a breakdown point have been proposed (e.g., Genton \& Lucas, 2003), but no details are given here.

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

When comparing two or more groups, the most common strategy is to use a single measure of location, and the median or 0.5 quantile is an obvious choice. It can be highly advantageous to compare other quantiles as well, but the motivation for doing this is best explained in Chapter 5. For now, attention is focused on estimating quantiles and the associated standard error.

There are many ways of estimating quantiles, comparisons of which are reported by Parrish (1990), Sheather and Marron (1990), as well as Dielman, Lowry, and Pfaffenberger (1994). Here, two are described and their relative merits are discussed.
For any $q, 0<q<1$, let $x_q$ be the qth quantile. For a continuous random variable, or a distribution with no flat spots, $x_q$ is defined by the equation $P\left(X \leq x_q\right)=q$. This definition is satisfactory in the sense that there is only one value that qualifies as the qth quantile, so there is no ambiguity when referring to $x_q$. However, for discrete random variables or distributions with flat spots, special methods must be used to avoid having multiple values that qualify as the qth quantile. There are methods for accomplishing this goal, but they are not directly relevant to the topics of central interest in this book, at least based on current technology, so this issue is not discussed. ${ }^1$

Setting $m=[q n+0.5]$, where $[q n+0.5]$ is the greatest integer less than or equal to $q n+0.5$, the simplest estimate of $x_q$ is
$$\hat{x}q=X{(m)}$$
the mth observation after the data are put in ascending order. For example, if the goal is to estimate the median, then $q=1 / 2$, and if $n=11$, then $m=[11 / 2+0.5]=6$, and the estimate of $x_{.5}$ is the usual sample median, M. Of course, if $n$ is even, this estimator does not yield the usual sample median, it is equal to what is sometimes called the upper empirical cumulative distribution function estimator.

# 假设检验代写

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

$$\hat{x} q=X(m)$$

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国英国加拿大澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|假设检验代写hypothesis testing代考|STAT101

statistics-lab™ 为您的留学生涯保驾护航 在假设检验hypothesis testing作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在假设检验hypothesis testing代写方面经验极为丰富，各种假设检验hypothesis testing相关的作业也就用不着 说。

• 时间序列分析Time-Series Analysis
• 马尔科夫过程 Markov process
• 随机最优控制stochastic optimal control
• 粒子滤波 Particle Filter
• 采样理论 sampling theory

Probability gives a way of measuring how likely an event is to occur in random sampling. In the last subsection you learned that a probability is always greater than or equal to 0 and always less than or equal to 1 . The following example and activity use data on truancy to help you become more familiar with the idea of probability. The same data is then used to explore another property of probability.Table 3 shows some invented data on truancy in two schools, A and B, that contained 200 and 100 pupils, respectively.

We shall use the table to answer the following questions.

1. If a child is selected at random from these two schools, what is the probability that this child was absent through truancy for fewer than 5 days?
2. If a child is selected at random from these two schools, what is the probability that this child is at School $\mathrm{A}$ and was absent through truancy for fewer than 5 days?
3. If a child is selected at random from School A, what is the probability that this child was absent through truancy for fewer than 5 days?
Let $T$ stand for the event that a child selected at random was absent through truancy for fewer than 5 days, and let $A$ stand for the event that the child attends School A.
4. Here the probability is $P(T)$. Now
\begin{aligned} P(T) & =\frac{\text { total number of children absent for }<5 \text { days }}{\text { total number of children }} \ & =\frac{150}{300}=0.5 . \end{aligned}
So there is a probability of $0.5$ that a child picked at random from these two schools was absent through truancy for fewer than 5 days.
5. Here the probability is that both events $T$ and $A$ occur. This is $P(T$ and $A)$, which is an extension of our notation for the probability of an event. (It means the probability that both $T$ and $A$ occur. In this case, the event ‘ $T$ and $A$ ‘ occurs if a child is absent through truancy for fewer than 5 days and also attends School A.) From Table 3, we see that 108 children attended School A and were absent through truancy for fewer than 5 days. So
\begin{aligned} P(T \text { and } A) & =\frac{\text { total number of children satisfying both } T \text { and } A}{\text { total number of children }} \ & =\frac{108}{300}=0.36 . \end{aligned}

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

We have seen that probabilities are added when we have the ‘or’ linkage, and want $\mathrm{P}(A$ or $B)$. We next consider how to determine probabilities when we have an ‘and’ linkage, and want $\mathrm{P}(A$ and $B)$. We use the notion that $\mathrm{P}(A$ and $B)$ is the proportion of the time that $A$ and $B$ both happen.

A restaurant offers a two-course set lunch. There are three choices for the first course – soup, pâté or salad – and two choices for the second course beef or pasta. The different meal-combinations are shown in Figure 3.

The diagram in Figure 3 is referred to as a tree. Starting at the left of the figure, we can follow one of three lines – branches – to choose a first course (soup, pâté or salad). From each first course we can follow one of two lines – sub-branches – to choose the second course (beef or pasta). Thus there are $3 \times 2=6$ different paths we can follow, corresponding to the six possible meal combinations: soup-beef, soup-pasta, pâté-beef, pâté-pasta, salad-beef and salad-pasta.
Suppose, now, that we choose a first course at random and also choose the second course at random. Then each of these six possibilities is equally likely. Thus the proportion of time we choose, say, salad followed by beef would be one-sixth, so
$$P(\text { salad and beef combination })=\frac{1}{6} \text {. }$$
Notice that there is a choice of three first courses, so if the choice is made at random,
$$P(\text { salad for first course })=\frac{1}{3} .$$
And, as there are two choices for the second course,
$$P(\text { beef for second course })=\frac{1}{2} \text {. }$$

Consequently, in this example
$P($ salad and beef combination $)=P($ salad $) \times P($ beef $)$.
Extending Example 3 is helpful, so suppose that there are four choices for the first course – soup, salad, pâté and prawns – and five choices for the second course – beef, chicken, fish, pasta and quiche. Following similar reasoning to Example 3, there are $4 \times 5=20$ different meal combinations.

# 假设检验代写

1. 如果从这两所学校中随机抽取一个孩子，这个孩子旷课少于 5 天的概率是多少?
2. 如果从这两所学校中随机抽取一个孩子，这个孩子在学校的概率是多少 $\mathrm{A}$ 并且因旷课而缺勤少于 5 天?
3. 如果从 $A$ 学校随机抽取一名儿童，该儿童旷课少于 5 天的概率是多少? 让 $T$ 代表随机选择的孩子因旷课少于 5 天而缺席的事件，并让 $A$ 代表孩子就读学校 $\mathrm{A}$ 的事件。
4. 这里的概率是 $P(T)$. 现在
$$P(T)=\frac{\text { total number of children absent for }<5 \text { days }}{\text { total number of children }}=\frac{150}{300}=0.5 .$$
所以有概率 $0.5$ 从这两所学校随机挑选的一个孩子因旷课不到 5 天而缺勤。
5. 这里的概率是两个事件 $T$ 和 $A$ 发生。这是 $P(T$ 和 $A)$ ，这是我们对事件概率表示法的扩展。（这意味 着两者的概率 $T$ 和 $A$ 发生。在这种情况下，事件 ‘ $T$ 和 $A$ ‘ 如果一个孩子因旷课少于 5 天而缺勤并且也 在学校 $\mathrm{A}$ 上学，则会出现这种情况。) 从表 3 中，我们看到有 108 名儿童在学校 $\mathrm{A}$ 上学并且因旷课 少于 5 天而缺勤。所以
$$P(T \text { and } A)=\frac{\text { total number of children satisfying both } T \text { and } A}{\text { total number of children }}=\frac{108}{300}=0.36 \text {. }$$

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

$$P(\text { salad and beef combination })=\frac{1}{6} \text {. }$$

$$P(\text { salad for first course })=\frac{1}{3} .$$

$$P(\text { beef for second course })=\frac{1}{2} .$$

$$P(\text { 沙拉和牛肉组合 })=P(\text { 沙拉 }) \times P(\text { 牛肉 }) \text {. }$$

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国英国加拿大澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|假设检验代写hypothesis testing代考|BSTA611

statistics-lab™ 为您的留学生涯保驾护航 在假设检验hypothesis testing作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在假设检验hypothesis testing代写方面经验极为丰富，各种假设检验hypothesis testing相关的作业也就用不着 说。

• 时间序列分析Time-Series Analysis
• 马尔科夫过程 Markov process
• 随机最优控制stochastic optimal control
• 粒子滤波 Particle Filter
• 采样理论 sampling theory

## 统计代写|假设检验代写hypothesis testing代考|Analysing the data

We have now decided on a specific question to investigate and we need to collect some data. This unit is mainly about analysing dlata that have already been collected, but it is worth spending a little time thinking about exactly what data should be collected. We can assume that we have a sampling frame consisting of all state-funded secondary schools in the East of England and the number of pupils they have. We can therefore pick out large schools, and we have arbitrarily defined these to be schools with 1000 or more pupils. We can then select a random sample of these schools. A sample size of 12 has been chosen.We now want a single number to summarise the amount of truancy for each of the 12 schools. First we must consider what we mean by truancy. If a child skips school to go to the shops, then they are playing truant, while if they miss school because they are ill in bed, then they are not.

Write down three reasons that a child might miss school – one that is definitely truancy, one that is definitely not truancy, and one that might or might not be truancy, depending on circumstances.

A school in Colorado photographed in 1915 during the season to harvest beet – only five pupils are at school while another thirty-five are absent because they are helping with the beet work.

A clear definition of truancy is needed if we are to gather truancy data for the different schools. The definition must take account of what data can be gathered, otherwise the definition may not be useful. In the next activity you are asked to think about how data related to truancy might be collected and used.Think of two possible ways in which data on truancy in a particular school could be collected and truancy in the school measured. They should be feasible methods which will not occupy too much of the teachers’ time.When gathering data, precise definitions are needed. Hence the UK government collects data, not on truancy, but on ‘unauthorised absence from school’. An unauthorised absence is absence without permission from a teacher or other authorised representative of the school. Records are kept of when permission for absence has been given (which would be retrospectively in the case of illness), so unauthorised absence is a well-defined, documented quantity. It is clearly closely related to truancy. Indeed, when the government publishes statistics on unauthorised absences from school, television and newspapers refer to them as truancy rates. We shall do the same.

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

The easiest way of thinking about probability is to equate it to proportion: the probability that a particular event will happen is the proportion of the time that it is expected to happen. When we toss a fair (unbiased) coin, for example, there is a fifty-fifty chance that the coin will land ‘heads’ because half the time it should land ‘heads’ and half the time it should land ‘tails’. That is, the proportion of time that the outcome should be heads is $\frac{1}{2}$, so the probability that the outcome will be heads is $\frac{1}{2}$.
(In practice, of course, you can only toss a coin a finite number of times, and it is very unlikely to land ‘heads’ exactly half the time. For example, if you toss it 600 times, then there is little chance that it will land ‘heads’ exactly 300 times. However, if you toss a coin an enormous number of times, the proportion of ‘heads’ should be very close to $\frac{1}{2}$.) Similarly, if a die is fair, then each of its six sides is equally likely to be the outcome when it is rolled. Thus, for example, the proportion of rolls that should result in a 4 is $\frac{1}{6}$, so the probability of rolling a 4 is $\frac{1}{6}$.

You met the ideas of random selection and random sampling in Unit 4. With random sampling, each member of the population is equally likely to be included in the sample. In particular, if a person or item is picked at random from a population, each member of the population is equally likely to be the one that is picked. We shall use these ideas to begin our investigation of probability.Now suppose that a student is selected at random from the university. Using the notion that probability equates to proportion, various probabilities relating to the student can be calculated. For example, the table gives the number of students who are female (2789) and the total number of students (6082). Hence we can determine the probability that the selected student is female by calculating the proportion of students who are female, as follows.

# 假设检验代写

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

（当然，在实践中，你只能抛硬币有限次，而且恰好有一半的时间“正面朝上”的可能性很小。例如，如果你抛 600 次，那么几乎没有机会它会恰好出现 300 次“正面朝上”。但是，如果你掷硬币的次数非常多，“正面朝上”的比例应该非常接近12.) 同样，如果一个骰子是公平的，那么它的六个面中的每一个面都同样可能是掷骰子时的结果。因此，举例来说，结果为 4 的掷骰比例为16, 所以掷出 4 的概率是16.

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国英国加拿大澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|假设检验代写hypothesis testing代考|BSTA511

statistics-lab™ 为您的留学生涯保驾护航 在假设检验hypothesis testing作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在假设检验hypothesis testing代写方面经验极为丰富，各种假设检验hypothesis testing相关的作业也就用不着 说。

• 时间序列分析Time-Series Analysis
• 马尔科夫过程 Markov process
• 随机最优控制stochastic optimal control
• 粒子滤波 Particle Filter
• 采样理论 sampling theory

## 统计代写|假设检验代写hypothesis testing代考|Clarifying the question

In Section 1 we consider what is meant by the question
How often do pupils truant?
Notice that this question refers implicitly to whole populations: for example, all schools in a particular area. We are usually not directly interested in how the children in one particular school behaved. However, it is often impossible, or at least not feasible, to collect data from the whole population. Instead we select a random sample of data. It might be a random sample of schools or of children. The sample is analysed by the methods we learned in earlier units, and we then need to decide how the results obtained from the sample apply to the whole population.
Statistical inference makes inferences about a population on the basis of data drawn from that population.
The above question about truancy may well have arisen from more general questions, such as:
Why do some pupils learn very little? Are we using good ways of teaching? Does the quality of my child’s education depend on where I live?

However, these latter questions can only be tackled if they are first made more precise. Hence, rather than simply posing a question, we will often need to clarify it, and we may need to clarify it more than once as we learn more about the problem. In earlier units we used the modelling diagram shown in Figure 1 as a framework for how we explore and summarise batches of data.

## 统计代写|假设检验代写hypothesis testing代考|The question to be clarified

As we saw in earlier units, statistics is good at answering questions that require a numerical answer. However, the question for this unit is a very vague question. For example, we might be interested in how much particular children truant, or we might want to compare truancy at different schools.
First, suppose we were looking at particular children.
Activity 1 Factors affecting a child’s truancy
Spend a few minutes thinking about what factors might affect how much a child plays truant. Then write down three factors that you think might be relevant.
Suppose a child psychologist is helping a particular child with a truancy problem. The psychologist would want to know the child’s attendance record and factors about the child’s circumstances that can influence truancy. The psychologist would then consider these factors and see if any pattern from the attendance record supported a given factor.
The same approach is followed if you move from considering individual truancy to truancy associated with different schools. We shall concentrate on looking at patterns with regard to schools, not individual children.
There are many different schools, and the amount of truancy will vary greatly. One of the interesting questions is whether different types of school have different amounts of truancy.
Activity 2 Factors affecting truancy in a school
Write down three factors that might affect the amount of truancy in a school.

Age of children is one of the most important factors in truancy figures. There is much less truancy at primary schools than at secondary schools. Young children are more likely to be taken to school by their parents, and also, since they are usually with the same class teacher all the time, truancy would be more easily noticed and could be followed up more quickly. We shall concentrate on secondary schools.
As you saw in the solution to Activity 2, there are still many factors that may affect truancy rate even after we have allowed for age to some extent by looking only at secondary schools. They include type of school, location of school and size of school, and there are also other factors, such as the attitude of the teachers, which are more difficult to measure. We shall look at several of these factors in the course of the unit, but we shall start with size of school.

# 假设检验代写

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国英国加拿大澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。