Statistics 简明教程
Statistics - One Proportion Z Test
检验统计量是一个 z 值(z),由下式定义。 ${z = \frac{(p - P)}{\sigma}}$ 其中 P 是零假设中总体比例的假设值,p 是样本比例,而 ${\sigma}$ 是抽样分布的标准差。
The test statistic is a z-score (z) defined by the following equation. ${z = \frac{(p - P)}{\sigma}}$ where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and ${\sigma}$ is the standard deviation of the sampling distribution.
检验统计量被定义并由下式给出:
Test Statistics is defined and given by the following function:
Formula
其中——
Where −
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${z}$ = Test statistics
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${n}$ = Sample size
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${p_o}$ = Null hypothesized value
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${\hat p}$ = Observed proportion
Example
Problem Statement:
Problem Statement:
一项调查称,十分之九的医生向患有头痛的患者推荐阿司匹林。为了检验这一说法,随机抽取了 100 名医生进行调查。在这 100 名医生中,有 82 人表示他们推荐服用阿司匹林。这一说法准确吗?使用 alpha = 0.05。
A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim, a random sample of 100 doctors is obtained. Of these 100 doctors, 82 indicate that they recommend aspirin. Is this claim accurate? Use alpha = 0.05.
Solution:
Solution:
定义零假设和备择假设
Define Null and Alternative Hypotheses
此处 Alpha = 0.05。使用 alpha 为 0.05 进行双尾检验,我们期望我们的分布看起来像这样:
Here Alpha = 0.05. Using an alpha of 0.05 with a two-tailed test, we would expect our distribution to look something like this:

这里,我们在每个尾部有 0.025。在我们的 z 表中查找 1 - 0.025,我们发现临界值为 1.96。因此,该双尾检验的决策规则为:如果 Z 小于 -1.96 或大于 1.96,则拒绝原假设。计算检验统计:
Here we have 0.025 in each tail. Looking up 1 - 0.025 in our z-table, we find a critical value of 1.96. Thus, our decision rule for this two-tailed test is: If Z is less than -1.96, or greater than 1.96, reject the null hypothesis.Calculate Test Statistic:
z = -2.667,故结果为我们应该拒绝原假设,从而得出结论,9/10 医生向其患者推荐阿司匹林的说法不准确,z = -2.667,p < 0.05。
As z = -2.667 Thus as result we should reject the null hypothesis and as conclusion, The claim that 9 out of 10 doctors recommend aspirin for their patients is not accurate, z = -2.667, p < 0.05.