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AgnesWu · 2023年06月02日

两个概念的区分

NO.PZ2017092702000111

问题如下:

For a two-sided confidence interval, an increase in the degree of confidence will result in:

选项:

A.

a wider confidence interval.

B.

a narrower confidence interval.

C.

no change in the width of the confidence interval.

解释:

A is correct.

As the degree of confidence increases (e.g., from 95% to 99%), a given confidence interval will become wider. A confidence interval is a range for which one can assert with a given probability 1 – α, called the degree of confidence, that it will contain the parameter it is intended to estimate.

随着置信度的增加(例如,从 95% 到 99%),给定的置信区间将变得更宽。 置信区间是一个范围,人们可以以给定的概率 1 – α(称为置信度)并代表它会包含我们要估计的参数。

我理解的两个概念:

confidence interval:μ±δ

confidence level/degree:置信度,为68%、90%……etc.


所以这道题我选了B,求解答



1 个答案

星星_品职助教 · 2023年06月02日

同学你好,

confidence interval应为:μ ± critical value*σ 。

critical value由degree of confidence(confidence level)决定,例如90%的confidence level对应±1.65,95%对应±1.96.

所以题干中说degree of confidence增加,相当于critical value变大,会导致confidence interval变宽。即A选项。

AgnesWu · 2023年06月02日

审题不仔细,我看成degree of size了,谢谢

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