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𝒜𝒩𝒥𝒜 安雅🎃 · 2021年09月15日

检验统计量的分子问题

  1. CFA I
  2. Quantitative

NO.PZ2018062016000132

问题如下：

Claire believes that the mean price of the commercial residential building is greater than $155,000. The population standard deviation is $25,000. A random sample of 36 commercial residential buildings in the area has a mean price of $159,750. Claire conduct the hypothesis test at a 1% level of significance. The value of the calculated test statistic is closet to:

选项：

A.

1.14.

B.

0.19.

C.

1.33.

解释：

A is correct. This is a one-tailed hypothesis since the alternative hypothesis only allows values greater than the hypothesized value. z=159750-155000/(25000/6)=1.14



我用上方公式算对了这题。但我不明白分子为什么不可以是the hypothesized value减去X̄？


如果是要衡量the hypothesized value在分布上离均值X̄多远，既然分布是左右对称，【the hypothesized value减去X̄再除以标准误】和【X̄减去the hypothesized value再除以标准误】，算出来的数值只是相差了一个正负号。我该怎么理解公式的分子【X̄减去the hypothesized value】的意思？

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已采纳答案

星星_品职助教 · 2021年09月16日

同学你好，

这个公式相当于是正态分布标准化。根据中心极限定理，X bar服从正态分布，且均值为总体均值μ0，标准差为总体标准差σ除以根号n。所以根据标准化的公式代入就是这个顺序。

简单看一下就行，这个逻辑不会去考，原版书上也没有。

这类“为什么一个公式是这样子的”的问题没有必要去纠结。所有公式都是数学证明出来的，直接应用即可。

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NO.PZ2018062016000132 问题如下 Claire believes ththe mepriof the commerciresintibuilng is greater th$155,000. The population stanrviation is $25,000. A ranm sample of 36 commerciresintibuilngs in the area ha mepriof $159,750. Claire conthe hypothesis test a 1% level of significance. The value of the calculatetest statistic is closet to: A.1.14. B.0.19. C.1.33. A is correct. This is a one-tailehypothesis sinthe alternative hypothesis only allows values greater ththe hypothesizevalue. z=159750-155000/(25000/6)=1.14 这个25000不是总体样本方差嘛？population不是总体方差嘛？请老师解惑下。

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