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Captain America · 2022年09月02日

请问查T表同样是90%，这里单尾和双尾分别查什么数字？

  1. CFA I
  2. Quantitative

NO.PZ2017092702000113

问题如下：

For a sample size of 37, 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.

8.5480.

B.

8.6970

C.

8.8456.

解释：

B is correct.

The confidence interval is calculated using the following equation:X‾±tα/2sn\overline X\pm t_{\alpha/2}\frac s{\sqrt n}

Sample standard deviation (s) = 245.55\sqrt{245.55} = 15.670.

For a sample size of 37, degrees of freedom equal 36, so t0.05 = 1.688.

The confidence interval is calculated as：


Therefore, the interval spans 120.5785 to 111.8815, meaning its width is equal to approximately 8.6970. (This interval can be alternatively calculated as 4.3485 × 2).

样本标准差的计算如下：

245.55\sqrt{245.55} = 15.670.

当样本=37，自由度=36，那么 t0.05 = 1.688.

置信区间计算如下：


因此，置信区间为：111.8815 - 120.5785，这意味着其宽度大约等于 8.6970。 （这个区间也可以计算为 4.3485 × 2）。

是单尾查0.05，双尾查0.1吗？这个单尾表和双尾表搞不清楚横向取值规则的区别

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星星_品职助教 · 2022年09月03日

同学你好，

教材给出的t分布表为单尾t表。

1）如果使用此表，最终要落到单尾的面积是多少。

本题90% confidence interval对应单尾为5%，即查5%和自由度36所对应的数值（见截图）。

单尾t表适用于绝大多数的题目。

2）如果查的是双尾t表，则要对应双尾面积10%，这种题目非常少，在Mock里偶尔出现过。

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