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胖婷肥周 · 2022年07月12日

老师这个解题步骤错在哪里？

  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.

我算出了1.91，然后用1.91去跟置信区间的关键值做比较。这个关键值，我看解题里面是1.65，但是5%是单尾的吖，为什么还是1.65呢？双尾±1.65吖。所以，我找的是t分布，单尾5%的，值是1.68。然后，1.91是大于1.68的，也就是在他的j Object的区间里，所以拒绝原假设，应该所以 H0≤26%是错误的。那么就是均值＞26%是正确呢，这样不是应该选择B吗？

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1 个答案

星星_品职助教 · 2022年07月13日

同学你好，

1）1.65对应的是正态分布下，单尾面积为5%时的情况；

2）本题也可以使用t检验的关键值，结论同样是test statistic＞critical value，所以要拒绝原假设。

根据题干，可得出原假设为H0：μ≤26%，

故最终结论为the mean of bond B is significant greater than 26%

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