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marciaaa · 2022年04月03日

老师您好，这里用z table查表的话带入的值是0.05（因为是10%除以2），得到的值是0.5199，请问我的思路是哪里出问题了呢？

  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%

老师您好，这里用z table查表的话带入的值是0.05（因为是10%除以2），得到的值是0.5199，请问我的思路是哪里出问题了呢？

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星星_品职助教 · 2022年04月03日

同学你好，

①10%置信区间对应左侧的尾部面积为5%，此时应该是P(critical value)=0.05，而不是P(0.05)=critical value

所以，正确的查表方式应为在表中找到0.05这个数字（下图中蓝色部分），然后反向对应出此时的critical value（下图中红色部分），可得到此时critical value在-1.64和-1.65之间。可以取-1.645或直接取-1.65.


②10%置信区间对应右侧的尾部面积为5%，此时左侧面积为95%。按照上述逻辑，此时查表应该去找P(critical value)=0.95，就可以得到+1.645或者四舍五入为+1.65，如下：

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