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今日打卡 · 2021年03月08日

为什么不用讲义中的这种方法?讲义中的方法只针对于标准正态分布么?

NO.PZ2015120604000117

问题如下:

A random sample is 100 CFA candidate's exam scoring. The mean of the scoring is 64. The standard deviation of the population scoring is 15 . The distribution is sopposed to be normal. The 95% confidence interval for the population mean should be:

选项:

A.

61.06 to 66.94.

B.

61.06 to 69.94.

C.

65.06 to 66.94.

解释:

A is correct.

Because the variance of the population is know and n ≥ 30,so The confidence interval is:

x¯ ± z α/2 (σ/ n )

z α/2 = z 0.025 =1.96

64 ± 1.96(15/10) = 64 ± 2.94 = 61.06 to 66.94.

1 个答案

星星_品职助教 · 2021年03月08日

同学你好,

①你列举的讲义上的解法应用的是正态分布下置信区间的公式,这适用于所有的正态分布(见讲义附图)

②这道题所用的方法和你提供的讲义上的方法是一致的。其中均值为样本均值64,标准差为样本均值标准差(即标准误)=15/√100=1.5,所以代入置信区间公式即为 64±1.96×1.5,得到[61.06,66.94]

③如果做出来的结果不一致,可以检查一下是不是样本均值的标准差(应该代入standard error=1.5)错误的代入了总体标准差15。


讲义附图:两道题目都用的是以下讲义上的这个公式:

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NO.PZ2015120604000117 问题如下 A ranm sample is 100 CFA cante's exscoring. The meof the scoring is 64. The stanrviation of the population scoring is 15. The stribution is supposeto normal. The 95% confinintervfor the population meshoulbe: A.61.06 to 66.94. B.61.06 to 69.94. C.65.06 to 66.94. A is correct.Because the varianof the population is know ann ≥ 30,so The confinintervis: x¯ ± z α/2 (σ/ n ) z α/2 = z 0.025 =1.96 64 ± 1.96(15/10) = 64 ± 2.94 = 61.06 to 66.94.因为样本方差已知且n 30,我们直接使用置信区间计算64 ± 1.96(15/10) = 64 ± 2.94 = 61.06 至 66.94.

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