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kekekeke · 2021年02月21日

老师请教一下：

NO.PZ2017092702000113

问题如下：

For a sample size of 17, with a mean of 116.23 and a variance of 245.55, the width of a 90% confidence interval using the appropriate t-distribution is closest to:

选项：

A.

13.23.

B.

13.27.

C.

13.68.

解释：

B is correct.

The confidence interval is calculated using the following equation: $\overline X\pm t_{\alpha/2}\frac s{\sqrt n}$ Sample standard deviation (s) = $\sqrt{245.55}$ = 15.670. For a sample size of 17, degrees of freedom equal 16, so t_0.05= 1.746. The confidence interval is calculated as

$116.23\text{ }\pm\text{ }1.746\frac{15.67}{\sqrt{17}}\text{ }=\text{ }116.23\text{ }\pm\text{ }6.6357$ Therefore, the interval spans 109.5943 to 122.8656, meaning its width is equal to approximately 13.271. (This interval can be alternatively calculated as 6.6357 × 2).

在查表或做题的时候，怎么判别是单尾还是双尾呢？比如说这题，90%的level查表的时候就要查0.05（不是太懂），谢谢！

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星星_品职助教 · 2021年02月21日

同学你好，

在数量这个学科中，“置信区间”都处于分布的中间位置，左右各会留出一个“尾巴”。

以本题为例，90%的置信区间，说明两侧两个尾巴的总面积就是1-90%=10%。

此时我们看原版书附录的t分布表，表头说明：

Table of the Student’s t-Distribution (One- Tailed Probabilities)

这个“One- Tailed Probabilities”说明t表看的是单尾面积。所以90%置信区间对应的单尾面积为10%/2=5%。也就是查表的时候需要查的是p=0.05那一列，不能查p=0.10对应的那一列。

-----------------

但如果给出的是双尾t表，那么90%置信区间的关键值直接查p=0.10就可以了。

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