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Sallyrrr · 2024年06月03日

Z test不是要在知道variance的情况下才能用吗?不是很明白这道题

  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.

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1 个答案

品职助教_七七 · 2024年06月03日

嗨，努力学习的PZer你好：


当总体方差未知时，首选要用t test。但本题并没有t test的选项。

于是考虑其他条件，当n很大时，可以用z test来近似替代t test。本题检验的是bond B，对应的n为49（见表格中“sample size”），大于了30，所以可以使用z test。

上述的逻辑即为讲义表格中右下角的：n＞30时，可使用t test or z test

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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