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寒塘鹤影 · 2022年02月04日

为什么一定是单尾的呀

  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:Z=X-μSxn =(0.32-0.26)0.2249=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.

为什么一定是单尾的呀

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1 个答案

星星_品职助教 · 2022年02月04日

同学你好，

需要根据备择假设来判断：

本题要证明的是“whether the mean of bond B is greater than 26%”，要证明的放备择假设，即Ha：μ＞26%。

由此可以得到1）单尾检验；2）拒绝域在右尾。

同理，

如果备择假设为Ha：μ＜26%，则为单尾检验和拒绝域在左侧

如果备择假设为Ha：μ≠26%，则为双尾检验和拒绝域在两侧。

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