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四喜丸子 · 2023年08月01日

请老师解释一下C选项

NO.PZ2022071202000078

问题如下:

Question The confidence interval is most likely to be:

选项:

A.wider as the sample size increases. B.wider as the point estimate increases. C.narrower as the reliability factor decreases.

解释:

Solution

C is correct. A confidence interval for a parameter = Point estimate ± Reliability factor × Standard error. For example, the reliability factors for confidence intervals based on the standard normal distribution are 1.65 for 90% confidence intervals and 1.96 for 95% confidence intervals. For a given point estimate and standard error, the confidence interval will be narrower with a lower reliability factor.

A is incorrect. A larger sample size will reduce standard error making the confidence interval more narrow.

B is incorrect. The point estimate does not affect the width of the confidence interval.

(1)请老师解释一下C选项

(2)reliability factor 怎么理解

1 个答案

星星_品职助教 · 2023年08月02日

同学你好,

1)答案解析已经给出置信区间的公式:A confidence interval for a parameter = Point estimate ± Reliability factor × Standard error

所以reliability factor变小,该区间变窄。

2)reliability factor即critical value。例如答案解析中提到的正态分布下,90%置信区间对应的1.65、95%置信区间对应的1.96,都是reliability factor/critical value的例子。


对于有详细答案解析的题目,提问时请具体说明答案解析中不理解的地方。