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zoewong · 2022年04月04日

為什麼不用sample mean 15% - 10% /25%/10

  1. CFA I
  2. Quantitative

NO.PZ2015120604000130

问题如下：

We want to use z-statistic to construct confidence interval for a normally distribution. Assume the sample size is 100, sample mean is 15% and the standard deviation of sample is 25%. The significance level is supposed to be 10% , the confidence interval is  :

选项：

A.

- 10.88% to 19.13%.

B.

10.88% to 19.13%.

C.

10.88% to 20.57%.

解释：

B is correct.

In this case, we can know that the Confidence Interval=[Point Estimate +/- (reliability factor)*Standard error]=

x¯±zα/2σn=15%±1.65×25%100=10.88%,19.13%

為什麼不用sample mean 15% - 10% /25%/10

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已采纳答案

星星_品职助教 · 2022年04月04日

同学你好，

正确的置信区间公式如下。逐项代入题干中数据即可。

正态分布下，significance level为10%所对应的reliability factor（即critical value） 为1.65.



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