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安在 · 2022年10月13日

怎么知道是T的双尾分布呢

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.

（1）根据被择假设判断双尾，根据样本量＜30 且不知道总体方差，所以用T ----------对吗？

（2）1% 的T分位点又没有给出表怎么知道具体等于2.797呢？

（3）表格中 sample B 的信息是不是完全没有使用在本题？

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星星_品职助教 · 2022年10月14日

同学你好，

（1）根据被择假设判断双尾，根据样本量＜30 且不知道总体方差，所以用T ，对吗？---用t的原因是总体方差未知。在正态总体的前提下，小样本应该选择用t分布。

（2）1% 的T分位点又没有给出表怎么知道具体等于2.797呢？---可查原版书对应附表，该表可在学员资料下载处下载。

（3）表格中 sample B 的信息是不是完全没有使用在本题？---对

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