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银色羽毛 · 2022年10月07日

关于B选项还是看不懂

  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.

关于B选项，虽然有很多提问了还是看不懂。。为什么解析里面用到的是1.68这个数值，1.68对应的应该是双尾5%，可题目应该是单位，单尾5%对应的数值应该是95%的1.96不是吗？那么就应该是test-statistic  1.91小于1.96不是吗？结论就变成B正确了 我不明白我的思路哪里出了问题，麻烦指正

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1 个答案

星星_品职助教 · 2022年10月08日

同学你好，

数量中的关键值是基于正态分布下的置信区间给出的，要求背诵的三组关键值如下：

90%置信区间：±1.65-----由于数量科目的置信区间都是双尾的，所以这个值对应双尾面积10%，或单尾面积5%；

95%置信区间：±1.96-------对应单尾面积2.5%；

99%置信区间：±2.58-------对应单尾面积0.5%；

------

本题为单尾检验，所以单尾的面积就为significancel level=5%，也就是关键值应为1.65。1.96是双尾面积5%对应的关键值。


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