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梦梦 · 2024年11月09日

type 1 和type 2error

NO.PZ2023091601000051

问题如下:

An oil industry analyst with a large international bank has constructed a sample of 1,000 individual firms on which she plans to perform statistical analyses. She considers either decreasing the level of significance used to test hypotheses from 5% to 1%, or removing 500 state-run firms from her sample. What impact will these changes have on the probability of making Type I and Type II errors?

选项:

Level of significance decrease Reduction in sample size

A.

P(Type I error) increases P(Type I error) increases

B.

P(Type I error) decreases P(Type II error) increases

C.

P(Type II error) increases P(Type I error) decreases

D.

P(Type II error) decreases P(Type II error) decreases

解释:

A Type I error is the error of rejecting a hypothesis when it is true. A Type II error is the error of accepting a false hypothesis.

A decrease in the level of significance decreases P(Type I error) but increases P(Type II error). Reducing the sample size increases P(Type II error).

C为啥不对啊?C和B不是一个意思吗?

2 个答案
已采纳答案

pzqa27 · 2024年11月12日

嗨,努力学习的PZer你好:


第一条说的是“level of significance used to test hypotheses from 5% to 1%”significance level 降低,significance level 是α,它就是犯1类错误的概率,所以1类错误变小。

第二条说降低500样本容量,降低样本容量会让1类错误和2类错误都上升。

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努力的时光都是限量版,加油!

pzqa27 · 2024年11月11日

嗨,从没放弃的小努力你好:


不是一个意思啊,题目说了这个分析师有2个动作,第一是“ decreasing the level of significance used to test hypotheses from 5% to 1%”,第二个举措是“removing 500 state-run firms from her sample”

第一个举措是降低1类错误,第二个举措是增加2类错误。C刚好说反了

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努力的时光都是限量版,加油!

梦梦 · 2024年11月12日

哦哦,“Reducing the sample size increases P(Type II error).”减少样本-标准误增加-检验统计量变小,更容易在尾部,H0更容易被拒绝,应该是type 1变大,2变小吧?2为啥增加?哪里想错了吗

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