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ruby5ltc · 2022年06月29日

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  1. CFA I
  2. Quantitative

NO.PZ2015120604000145

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 A is equal to 22%,

which of the following conclusion is least appropriate (significant level=1%) ?

选项：

A.

The null hypothesis can be rejected.

B.

It is appropriate to use a two-tailed t-test.

C.

The test statistic value is 1.333.

解释：

A is correct.

The null hypothesis: H0: μ=22%.

Because the sample size is 25, which is less than 30, so it is appropriate to use the two-tailed t-test.

t=（X−μ0）sn=(0.26−0.22)0.1525=1.33t=\frac{（X-\mu_0）}{\frac s{\sqrt n}}={\textstyle\frac{(0.26-0.22)}{\textstyle\frac{0.15}{\sqrt{25}}}}=1.33

t at α= 0.01= ±2.797;

Because -2.797 <1.333<+2.797, therefore, H0 cannot be rejected.

t为什么是±2.797;

t难道不是±2.58吗？

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2 个答案

星星_品职助教 · 2022年07月01日

@ruby5ltc

总体方差未知，用t分布。

星星_品职助教 · 2022年07月01日

同学你好，

2.58是正态分布下对应的关键值。

本题为t分布，需要查表求关键值，即2.797

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