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哇 · 2021年07月29日

No.PZ2017092702000113 (选择题) 这道题在考试的时候题目会给出1.746这个数字吗？

  1. CFA I
  2. Quantitative

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: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 17, degrees of freedom equal 16, so t0.05 = 1.746.

The confidence interval is calculated as：


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).

样本标准差的计算如下：

245.55\sqrt{245.55} = 15.670.

当样本=17，自由度=16，那么 t0.05 = 1.746.

自信区间计算如下：


因此，自信区间为：109.5943 - 122.8656，这意味着其宽度大约等于 13.271。 （这个区间也可以计算为 6.6357 × 2）。

这道题在考试的时候题目会给出1.746这个数字吗？

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星星_品职助教 · 2021年07月30日

同学你好，

大概率不会直接给。

1.746是查t表所得的值，查表是需要掌握的。考试的时候会给出相关的信息，例如同时给三四个关键值要求考生自行选出应使用的那一个。

对于日常练习而言，直接用原版书后表进行查找练习就可以了。原版书的表格在“资料下载”处提供下载。

哇 · 2021年07月30日

谢谢老师 查表没有问题 只要考试的时候会给表格不用背出来就好

星星_品职助教 · 2021年07月30日

@哇

可以放心~考试时一定会给出表格相关信息的，不然就没法做了。

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