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Sophie · 2022年10月20日

关于标准差和标准误

  1. CFA I
  2. Quantitative

NO.PZ2015120604000147

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 B is greater than 26%,

which of the following conclusion is least appropriate (significant level=5%) ?

选项：

A.

It is approptiate to use the Z-test.

B.

The mean of bond B is not significant greater than 26%.

C.

It is a one-tailed test.

解释：

B is correct.

It is appropraite to ues the one-tailed Z-test because the sample size of bond B is bigger than 30.

The null hypothesis is: H0: μ ≤ 26%

The test statistic:


α= 5% indicates the critical value is equal to ±1.65.

Because 1.91>1.65, therefore, we should reject the null hypothesis.

请问老师在算Z statistic时是么时候用标准差什么时候用标准误呢？有点模糊不清了，请讲一下，谢谢！

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星星_品职助教 · 2022年10月20日

同学你好，

样本自身的离散程度为标准差。

样本均值的离散程度，即样本均值的标准差为标准误。

找准对应关系即可，例如本题分子上为样本均值，对应分母就应该是标准误。

Sophie · 2022年10月20日

什么是自身的离散程度？能举个例子吗？谢谢！

星星_品职助教 · 2022年10月20日

@Sophie

标准差衡量的是每个数据到均值的离散程度。类似的离散程度指标还有Range，MAD等。

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