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苏·Xu · 2023年06月29日

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.

样本量越大,估计越准确不是吗?那样置信区间会更宽啊。


比如90%的信心和99%的信心,99%的信心置信区间更宽啊

1 个答案

星星_品职助教 · 2023年06月29日

同学你好,

估计越准确,对应的置信区间越窄。所以A选项应该是narrower as...

99%信心的置信区间要比90%信心的置信区间宽,但不如90%的置信区间精确。

区间越窄,对于总体参数的估计越精确,相反,如果区间很宽,参数的估计就宽泛。一个极端的例子就是如果区间宽到极限,成为整条数轴,那么我们有100%的信心总体参数一定在负无穷到正无穷的区间里,但这种估计就完全没有精确度可言。