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醉清风 · 2020年01月08日

问一道题:NO.PZ2018062001000013

问题如下:

Tim, an analyst of an investment company, says "If we increase the sample size only, both the standard error and the confidence interval width will reduce. " Tim's statement is:

选项:

A.

correct.

B.

incorrect about confidence interval.

C.

incorrect about the standard error.

解释:

A is correct.

By increasing the sample size, the estimation of population parameter is more accurate. Therefore, the standard error will decrease, and confidence interval will become narrower.

不是当样本数量增加,N自由度也是增加,置信区间不是更宽吗?

1 个答案

星星_品职助教 · 2020年01月08日

同学你好,

从两个角度解答你这个问题。首先是这道题解题的思路是根据置信区间的公式如下:

由于n在分母上,所以n越大,置信区间是越窄。

另外,n上升会导致t分布的自由度上升。但自由度上升后会使得t的临界值也是减小的,可以拿原版书后的t表来验证一下。这个的原因是t在n增加后会趋近于正态分布,本来是比正态分布矮胖的,现在逐渐变“瘦”,对应区间也变窄了。


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