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Sayuri999 · 2022年05月09日

检验mean of bond A是否等于22%，为什么零假设是H0=22%？

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: $H_{0} : μ = 22 %.$

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

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

t at α= 0.01= ±2.797;

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

No.PZ2015120604000145 (选择题)

来源: 品职出题

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%) ?

题目中whether the mean of bond A is equal to 22%，为什么零假设是H0=22%而不是 Ha=22%？视频课里老师说相信的那个为备择假设，题目的意思为什么不是相信A的平均收益率为22%呢

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星星_品职助教 · 2022年05月10日

同学你好，

有一个快捷的判断方法：“等号”永远在原假设，所以“=”。“≥”，和“≤”这些带等号的只会在原假设里出现，不会出现在备择假设里。

备择假设里只会有≠，＞，和＜

从定性角度出发，当检验均值/方差是否等于一个确定的数的时候，原假设都是=，备择假设都是≠。不会有其他的情况出现，也不需要按照“是否相信”来判断。

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