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何珊 · 2021年11月10日

解题中阿尔法=0.01=+_2.797怎么来的？

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.

解题中阿尔法=0.01=+_2.797怎么来的？

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星星_品职助教 · 2021年11月10日

同学你好，

这个等式写的不是很规范。意思是±2.797是significance level=0.01时，对应的t分布关键值（critical value）。需要根据自由度（df=25-1=24）和significance level=0.01查表求得的。

t分布表可以从原版书附录找或者从学员资料下载处下载，如果对于如何查表有问题可以继续提问。

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