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Helen 🎈 · 2022年12月13日

为啥自由度是36呀

  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）。

课程中哪里讲了这个的老师能不能给学渣标一下啊谢谢

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1 个答案

星星_品职助教 · 2022年12月13日

同学你好，

置信区间考点下的：对于总体均值做区间估计，和后续假设检验考点下的：检验总体均值是否等于一个特定的数，这两个考点都涉及到用t分布，此时t分布的自由度为n-1。

主要原因是公式中有样本标准差s，此时t分布的自由度和s的自由度一致。


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