问一道题：NO.PZ2015120604000147 [ CFA I ]

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：

It is approptiate to use the Z-test.

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

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: $H_{0} : μ$ ≤ $26%$

The test statistic: $Z = \frac{X - μ}{\frac{S_{x}}{\sqrt{n}}}$ $= \frac{(0.32 - 0.26)}{\frac{0.22}{\sqrt{49}}} = 1.91$

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

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

不是“总体方差未知，t分布”吗？为什么选A？

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1 个答案

星星_品职助教 · 2020年06月01日

同学你好，

总体方差未知，用t分布没错。本题的首选也应该是t分布，但答案中并没有给t分布的选项，同时由于本题的sample size较大（N=49＞30），所以符合了中心极限定理的条件，可以用正态分布去近似替代t分布。

由于正态分布毕竟不是最优选择，所以也可以验证一下另外两个选项，由于B选项明显错误，直接选择B为least appropriate的就可以了。

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问一道题：NO.PZ2015120604000147 [ CFA I ]

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