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临江仙 · 2020年01月30日

问一道题:NO.PZ2019040801000025

问题如下:

Assuming the height of a tree in a forest follows a normal distribution, there are more than 10,000 trees. The sample size of test is 200, the 95% confidence interval of the sample mean of the height is 11 to 35 meters based on a z-statistic, the standard error of mean height is closest to:

选项:

A.

1.96.

B.

3.58.

C.

6.12.

D.

10.50.

解释:

C is correct.

考点:The central limit theorem (CLT)

解析:95%的置信区间是11到 35,z值是1.96.

平均数为0.5*(11+35)=23.所以置信区间是23 ± 1.96sx, sx是标准差。23+1.96sx等于35,sx等于6.12

查看之前的问题,发现回答说:置信区间是通过标准误 计算出来的。

请教,如何判断置信区间是通过标准误计算还是通过标准差计算。


如果不能区分的话,对于做题而言,非常有难度。

1 个答案

orange品职答疑助手 · 2020年02月04日

同学你好,应该是标准误。标准误=标准差/根号n 。这题解析是该修改下,谢谢同学的提醒。

XP · 2020年04月24日

标准差=6.12,那标准误应该是6.12/根号200 吧?所以是答案也错了?麻烦回答清楚吖。

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