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assignmentutor-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|Finding the chi-square values

Critical values for chi-square distribution are usually used to help and guide researchers making a decision about a hypothesis of interest. We can obtain chisquare critical values for various degrees of freedom $(d . f)$ and the level of significance $(\alpha)$ from Table $\mathrm{C}$ in the Appendix. Thus we need to prepare two values to use a chi-square table and obtain the required critical value; the two values are the degrees of freedom and the significance level. The first column on the left of Table C represents the degrees of freedom $(d . f)$ from 1 to $\infty$, while the first upper row represents the level of significance $(\alpha)$.

Example 5.1: Finding the critical value for the left-tailed chi-square test: Use a significance level of $0.01(\alpha=0.01)$ and degrees of freedom of $11(d . f=11)$ to obtain the chi-square critical value for the left-tailed chi-square test.

We can obtain the chi-square critical value for the left-tailed test as long as two values are provided, the two values are the degrees of freedom ” $d . f=11$ ” and significance level ” $\alpha=0.01$.”

• The first step in extracting the chi-square critical value is to specify the position of “d.f $=11$ ” in the first column of Table C, labeled d.f. Table $5.1$ is a portion of Table $\mathrm{C}$ in the Appendix.
• The second step is to specify the position of $1-\alpha=0.99$ (because the area under the chi-square curve is to the right of $\chi^2$ and the required value is to the left side, thus the required area equals to $1-\alpha$ ) in the first upper row (highlighted column) and then move on the column to the row labeled $d . f=11$ (highlighted row), the value that represents the point of intersection between $d . f=11$ and $1-\alpha=0.99$ is the $\chi^2$ critical value. One can observe that the $\chi_L^2$ critical value is $3.053$ as shown in Table $5.1$ (bold value).

This problem is a left-tailed test; thus the critical value for the left-tailed test is $\chi_L^2=\chi_{(1-a, d, f)}^2=\chi_{(1-0.01,11)}^2=\chi_{(0.99,11)}^2=3.053$.

Fig. $5.2$ shows the area to the left of $x_{(0.99,11)}^2=3.053$ (shaded area under the curve).

## 统计代写|假设检验代写hypothesis testing代考|Hypothesis testing for one-sample variance or standard deviation

Hypothesis testing about the variance or standard deviation can be carried out using a new test called a $\chi^2$ test.

Consider a random sample of size $n$ that is selected from a normally distributed population, a claim regarding the variance (standard deviation) value of the variable of interest can be tested employing the $\chi^2$ test for one sample variance (standard deviation) to make a decision regarding the variance (standard deviation) value. The mathematical formula for computing the test statistic value for one sample variance (standard deviation) employing the $\chi^2$ test is presented in Eq. (5.1).
$$\chi^2=\frac{(n-1) s^2}{\sigma_0^2}$$
Follow chi-square distribution with $(n-1)$ degrees of freedom, where $n$ : the sample size,
$s^2$ : the sample variance, and
$\sigma_0^2$ : the population variance.

Example 5.4: The concentration of total suspended solid of surface water: A researcher at an environmental section wishes to verify the claim that the variance of total suspended solids concentration (TSS) of Beris dam surface water is $1.25(\mathrm{mg} / \mathrm{L})$. Twelve samples were selected and the total suspended solids concentration was measured. The collected data showed that the standard deviation of total suspended solids concentration is $1.80$. A significance level of $\alpha=0.01$ is chosen to test the claim. Assume that the population is normally distributed.

The general procedure for conducting hypothesis testing can be used to make the decision regarding the variance of total suspended solids concentration in the surface water of Beris dam.
Step 1: Specify the null and alternative hypotheses
The population variance of total suspended solids concentration $\left(\sigma^2\right)$ is $1.25$; this claim should be under the null hypothesis because the claim represents equality $(=)$. If the variance of total suspended solids concentration of surface water is not equal to $1.25$, then two cases should be considered; in the first case, the variance of total suspended solids concentration is greater than $1.25$, and in the second case, the variance is less than $1.25$. The two cases (greater than and less than) can be represented mathematically as $\neq$. Thus we can write the two hypotheses (null and alternative) as presented in Eq. (5.2).

# 假设检验代写

## 统计代写|假设检验代写hypothesis testing代考|Finding the chi-square values

• 提取卡方临界值的第一步是指定“ $\mathrm{df}=11$ “在表 $\mathrm{C}$ 的第一列，标记为 df Table5.1是表的一部分 $\mathrm{C}$ 在附录中。
• 第二步，指定位置 $1-\alpha=0.99$ (因为卡方曲线下的面积在右边 $\chi^2$ 并且所需的值在左侧，因此所需的面积等于 $\left.1-\alpha\right)$ 在第一行 (突出显示的列) 中，然 后在该列上移动到标记为的行 $d . f=11$ (突出显示的行)，表示两者之间的交点的值 $d . f=11$ 和 $1-\alpha=0.99$ 是个 $\chi^2 |^2$ 临界值。可以观察到 $\chi_L^2$ 临界值为 $3.053$ 如表所示 $5.1$ (粗体值) 。
这个问题是一个左尾测试; 因此左尾检验的临界值为 $\chi_L^2=\chi_{(1-a, d, f)}^2=\chi_{(1-0.01,11)}^2=\chi_{(0.99,11)}^2=3.053$.
如图。5.2显示左边的区域 $x_{(0.99,11)}^2=3.053$ (曲线下的阴影区域)。

## 统计代写|假设检验代写hypothesis testing代考|Hypothesis testing for one-sample variance or standard deviation

$$\chi^2=\frac{(n-1) s^2}{\sigma_0^2}$$

$s^2$ : 样本方差，和
$\sigma_0^2$ : 总体方差。

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## MATLAB代写

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assignmentutor™您的专属作业导师
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