影响置信区间宽度的因素

Factors affecting the width of confidence intervals

样本量越大，估计量的标准误越小，于是置信区间的宽度越小。此外，对于采用t分布的区间估计，样本量还会影响t分布的自由度，进而影响置信区间。对一般的区间估计，如果不引进估计量的标准误的概念，样本对区间宽度仍然有影响。样本量越大，置信区间的宽度就越小，反之亦然。

• The larger the sample size, the smaller the standard error of the estimate, and thus the smaller the width of the confidence interval. In addition, for interval estimation using the t-distribution, the sample size also affects the degrees of freedom of the t-distribution, which in turn affects the confidence interval. For interval estimation in general, the sample still has an effect on the width of the interval if the concept of the standard error of the estimator is not introduced. The larger the sample size, the smaller the width of the confidence interval, and vice versa.

规定的置信度越高，那么置信区间就会变宽，但是相应地，准确度就会降低，反之亦然。

• The higher the confidence level specified, then the confidence interval becomes wider, but correspondingly, the accuracy decreases, and vice versa.

一般来说，样本数据的方差越大，对于相同的置信度，所需要的覆盖区间也就越宽。

• In general, for the same confidence level, the higher the variance of the sample data, the wider the required coverage interval.