## 统计代写|假设检验代写hypothesis testing代考|Testing one sample mean when the variance is unknown: P-value

We have studied hypothesis testing for one sample mean when the population variance is unknown and the sample size is small using the critical value (traditional) procedure for a t-test. The $P$-value procedure for one sample mean using a t-test will be illustrated employing the same examples presented in Chapter 3 , t-Test for one-sample mean, and solved using the critical value procedure.

The three situations of hypothesis testing are covered and the $P$-values are calculated.

Example 6.10: The concentration of trace metal iron in the air: Example $3.4$ is reproduced “A researcher at an environmental section wishes to verify the claim that the mean concentration of trace metal iron (Fe) on coarse particulate matter $\left(\mathrm{PM}_{10}\right)$ in the air is $0.36\left(\mu \mathrm{g} / \mathrm{m}^3\right)$ during the summer season of an equatorial urban coastal location. Twelve samples were selected, and the concentration of iron was measured. The collected data showed that the mean concentration of iron is $0.44$ and the standard deviation is $0.34$. A significance level of $\alpha=0.01$ is chosen to test the claim. Assume that the population is normally distributed.”

The five steps for conducting hypothesis testing employing the $P$-value procedure can be used to test the hypothesis regarding the mean concentration of trace metal iron on coarse particulate matter in the air during the summer season of an equatorial urban coastal location. The results of the $P$-value procedure will be compared with the critical value (traditional) procedure.
Step 1: Specify the null and alternative hypotheses
The two hypotheses regarding the mean concentration of iron on coarse particulate matter in the air are presented in Eq. (6.10).
$$H_0: \mu=0.36 \text { vs } H_1: \mu \neq 0.36$$
Step 2: Select the significance level $(\alpha)$ for the study
The level of significance is chosen to be $0.01$. The $\mathrm{t}$ critical values for a twotailed test with $\alpha=0.01$ and $d . f=12-1=11$, are $t_{\left(\frac{a}{2}, d . f\right)}=t_{\left(\frac{0.01}{2}, 12-1\right)}=\mp 3.106$.

## 统计代写|假设检验代写hypothesis testing代考|Testing one sample proportion: P-value

Hypothesis testing for one sample proportion using the critical value (traditional) procedure was studied in Chapter 4 , Z-test for one sample proportion. The $P$-value procedure for one sample proportion using a Z-test will be illustrated employing examples to cover various situations of hypothesis testing.

Example 6.13: Mineral water: Example $4.4$ is reproduced “A research group at a university wishes to verify the claim announced by a specific factory for mineral water which says that $98 \%$ of people are satisfied with the quality of mineral water. The research group selected 700 people randomly and record their responses, they found that 26 were not satisfied. Use the sample information to make a decision whether to support the claim or not. A significance level of $\alpha=0.01$ is chosen to test the claim. Assume that the population is normally distributed.”

The five steps for conducting hypothesis testing employing the $P$-value procédure can be used to test the hypothesis regarding the proportion of people who feel satisfied with the mineral water produced by the factory. The results of the $P$-value procedure will be compared with the critical value (traditional) procedure.
Step 1: Specify the null and alternative hypotheses
The two hypotheses regarding the proportion of people who feel satisfied with the mineral water produced by the factory are presented in Eq. (6.13)
$$H_0: p=0.98 \text { vs } H_1: p \neq 0.98$$
Step 2: Select the significance level $(\alpha)$ for the study
The level of significance is chosen to be $0.01$. The $\mathrm{Z}$ critical values for a twotailed test with $\alpha=0.01$ are $\pm 2.58$.

The two procedures will be used to solve this problem; namely the critical value and $P$-value procedures.
Step 3: Use the sample information to calculate the test statistic value
The test statistic value for the $\mathrm{Z}$-test is used to make a decision regarding the proportion of people who feel satisfied with the mineral water produced by the factory. The test statistic value using the Z-test formula was calculated to be $-3.78$.

Step 4: Calculate the $P$-value and specify the critical and noncritical regions for the study

The rejection and nonrejection regions using the critical values for testing the proportion of people who feel satisfied with the mineral water produced by the factory are presented in Fig. $6.13$ for the standard normal curve (shaded area: blue represents the $P$-value and orange represents the significance level).

# 假设检验代考

## 统计代写|假设检验代写假设检验代考|当方差未知时检验一个样本均值:p值

$$H_0: \mu=0.36 \text { vs } H_1: \mu \neq 0.36$$

## 统计代写|假设检验代写假设检验代考|检验一个样本比例:p值

$$H_0: p=0.98 \text { vs } H_1: p \neq 0.98$$

$\mathrm{Z}$ -test的测试统计值用于决定对工厂生产的矿泉水感到满意的人的比例。使用z检验公式计算的检验统计值为$-3.78$ .

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