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西红柿面 · 2023年09月30日

为什么A不选？

  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 appropriate 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.

我看助教都说了“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”。所以这道题应该用T分布啊，A说的是用Z分布，所以错了呀？

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星星_品职助教 · 2023年09月30日

本题就是选项里根本没有t分布，用不了t分布的情况，所以考虑N大于30时使用的z分布。

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