Statistics 简明教程
Statistics - One Proportion Z Test
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.
Test Statistics is defined and given by the following function:
Formula
其中——
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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:
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:
Define Null and Alternative Hypotheses
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：
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。