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275730944 · 2023年07月26日

置信区间5%对应的不应该是1.96吗这里为什么是1.65

  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.

置信区间5%对应的不应该是1.96吗这里为什么是1.65

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1 个答案

星星_品职助教 · 2023年07月26日

同学你好，

1）本题是假设检验，不是置信区间；

2）双尾假设检验的关键值和置信区间是相同的。即95%置信区间对应的关键值和significance level为5%的双尾检验关键值都是1.96。

3）本题为单尾检验，即单侧尾部面积为本题的significancel level 5%。单尾面积为5%为90%的置信区间的情况，所以关键值应为1.65.

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