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Nickyan · 2022年04月19日

原题中说significant level=1%，请问我们什么时候用阿尔法/2 ，two sided 不应该除以2吗

NO.PZ2015120604000145

问题如下：

Here is a table discribing sample statistics from two bonds' rate of return which are both normally distributed over the past decades. If an investor is considering whether the mean of bond A is equal to 22%,

which of the following conclusion is least appropriate (significant level=1%) ?

选项：

A.

The null hypothesis can be rejected.

B.

It is appropriate to use a two-tailed t-test.

C.

The test statistic value is 1.333.

解释：

A is correct.

The null hypothesis: $H_{0} : μ = 22 %.$

Because the sample size is 25, which is less than 30, so it is appropriate to use the two-tailed t-test.

$t=\frac{（X-\mu_0）}{\frac s{\sqrt n}}={\textstyle\frac{(0.26-0.22)}{\textstyle\frac{0.15}{\sqrt{25}}}}=1.33$

t at α= 0.01= ±2.797;

Because -2.797 <1.333<+2.797, therefore, H₀ cannot be rejected.

原题中说significant level=1%，请问我们什么时候用阿尔法/2 ，two sided 不应该除以2吗

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星星_品职助教 · 2022年04月19日

同学你好，

本题在查表时，实际用的就是α/2。流程如下：

由于本题为双尾检验，significance level=α=1%就相当于单侧尾部面积为α/2=0.5%，对应自由度25-1=24即可得到critical value=（±）2.797，如图。

如果是单尾检验，则significance level=1%就相当于单尾面积就是1%。这种情况下的critical value就是2.492了

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Vicky · 2022年04月19日

同学，您好！双尾检验用的是α，单尾检验用的是α/2 在这个题目中，因为样本量不到30个，所以要用t检验。利用公式计算检验统计量，分子是样本均值-检验均值。0.04。分母是标准误，标准差除以样本量的根号值0.15/根号25。检验统计量是1.33 没有落在拒绝域，不能拒绝原假设。

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Vicky · 2022年04月19日

抱歉，我说反了，以助教老师为准哈

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