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# 统计代写| 假设检验作业代写Hypothesis testing代考|How Confidence Intervals Work

##### 空白假设的早期选择

Paul Meehl认为，无效假设的选择在认识论上的重要性基本上没有得到承认。当无效假设是由理论预测的，一个更精确的实验将是对基础理论的更严格的检验。当无效假设默认为 “无差异 “或 “无影响 “时，一个更精确的实验是对促使进行实验的理论的一个较不严厉的检验。

1778年：皮埃尔-拉普拉斯比较了欧洲多个城市的男孩和女孩的出生率。他说 “很自然地得出结论，这些可能性几乎处于相同的比例”。因此，拉普拉斯的无效假设是，鉴于 “传统智慧”，男孩和女孩的出生率应该是相等的 。

1900: 卡尔-皮尔逊开发了卡方检验，以确定 “给定形式的频率曲线是否能有效地描述从特定人群中抽取的样本”。因此，无效假设是，一个群体是由理论预测的某种分布来描述的。他以韦尔登掷骰子数据中5和6的数量为例 。

1904: 卡尔-皮尔逊提出了 “或然性 “的概念，以确定结果是否独立于某个特定的分类因素。这里的无效假设是默认两件事情是不相关的（例如，疤痕的形成和天花的死亡率）。[16] 这种情况下的无效假设不再是理论或传统智慧的预测，而是导致费雪和其他人否定使用 “反概率 “的冷漠原则。

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• 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| 假设检验作业代写Hypothesis testing代考|Precision of the Estimate

Confidence intervals include the point estimate for the sample with a margin of error around the point estimate. The point estimate is the most likely value of the parameter and equals the sample value. The margin of error accounts for the amount of doubt involved in estimating the population parameter. The more variability there is in the sample data, the less precise the estimate, which causes the margin of error to extend further out from the point estimate. Confidence intervals help you navigate the uncertainty of how well a sample estimates a value for an entire population.

With this in mind, confidence intervals can help you compare the precision of different estimates. Suppose two studies estimate the same mean of 10. It appears like they obtained the same results. However, using $95 \%$ confidence intervals, we see that one interval is [5 15$]$ while the other is $\left[\begin{array}{ll}9 & 11\end{array}\right]$. The latter confidence interval is narrower, which suggests that it is a more precise estimate.

## 统计代写| 假设检验作业代写HYPOTHESIS TESTING代考|Graphical Representation

Let’s delve into how confidence intervals incorporate the margin of error. Like the previous sections, I’ll use the same sampling distribution that showed us how hypothesis tests work.

There are two critical differences between the sampling distribution graphs for significance levels and confidence intervals. The significance level chart centers on the null value, and we shade the outside $5 \%$ of the distribution. Conversely, the confidence interval graph centers on the sample mean, and we shade the center $95 \%$ of the distribution.The shaded range of sample means [267 392$]$ covers $95 \%$ of pling distribution. This range is the $95 \%$ confidence interv sample data.

We don’t really know whether our sample mean is near the population mean. However, we know that the sample mean is an unbiased estimate of the population mean. An unbiased estimate is one that doesn’t tend to be too high or too low. It’s correct on average. Confidence intervals are correct on average because they use sample estimates that are correct on average. Given what we know, the sample mean is the most likely value for the population mean.

Given the sampling distribution, it would not be unusual for other random samples drawn from the same population to have means that fall within the shaded area. In other words, given that we did obtain the sample mean of $330.6$, it would not be surprising to get other sample means within the shaded range.

If these other sample means would not be unusual, then we must conclude that these other values are also likely candidates for the population mean. There is inherent uncertainty when you use sample data to make inferences about an entire population. Confidence intervals help you gauge the amount of uncertainty in your sample estimates.

## 统计代写| 假设检验作业代写HYPOTHESIS TESTING代考|GRAPHICAL REPRESENTATION

If you want to determine whether your test results are statistically significant, you can use either p-values with significance levels or confidence intervals. These two approaches always agree.

The relationship between the confidence level and the significance level for a hypothesis test is as follows:
Confidence level $=1$ – Significance level (alpha)

For example, if your significance level is $0.05$, the equivalent confidence level is $95 \%$.

Both of the following conditions represent a hypothesis test with statistically significant results:

• The p-value is smaller than the significance level.
• The confidence interval excludes the null hypothesis value.
Further, it is always true that when the p-value is less than your significance level, the interval excludes the value of the null hypothesis.
In the fuel cost example, our hypothesis test results are statistically significant because the p-value $(0.03112)$ is less than the significance level (0.05). Likewise, the 95\% confidence interval $\left[\begin{array}{ll}267 & 394\end{array}\right]$ excludes the null hypothesis value (260). Using either method, we draw the same conclusion.

## 统计代写| 假设检验作业代写HYPOTHESIS TESTING代考|GRAPHICAL REPRESENTATION

• p 值小于显着性水平。
• 置信区间不包括原假设值。
此外，当 p 值小于显着性水平时，区间会排除原假设的值，这始终是正确的。
在燃料成本示例中，我们的假设检验结果具有统计显着性，因为 p 值(0.03112)小于显着性水平0.05. 同样，95% 置信区间[267394]排除原假设值260. 使用任何一种方法，我们都会得出相同的结论。

## 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。