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Ariel · 2023年01月18日

如果判断题目给的数是样本标准误还是总体标准差

  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.

  • 1、表格给出的是样本size，样本平均数，最后一个不应该是样本sd就直接是标准误了吗？怎么变成了总体标准差？做题要怎么判断题目给出的是总体还是样本？

2、假设这题给的22%就是标准误，是不是属于总体方差未知，就算样本大于30也要用t分布？

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星星_品职助教 · 2023年01月18日

同学你好，

1）题干给出的是sample的表，里面都是sample 1 / sample 2的对应值。不会有总体的参数。最后一列也是样本自身的 sample standard deviation。

标准误是样本均值（而非样本自身）的标准差，即标准误还需要在表里给出的sample standard deviation的基础上再除以根号n。所以本题求sample 2的standard error时，用的是表格中的22%再除以根号49；

2）由于本题给的22%是样本自身的标准差，和总体标准差没有关系。所以属于总体标准差（方差）未知的情况。优先使用t分布，只有t分布用不了时才考虑大于30的情况。

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