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Serein · 2022年05月17日

为什么这里要用Sx/根号n？ standard deviation of sample 不就是Sx（sample）吗？

  1. CFA I
  2. Quantitative

NO.PZ2015120604000137

问题如下：

Ida Lee and his team collect a lot of analysis of statistical data about the car market .According to the data, they come to the conclusion that the mean price of SUV is more than $46,435 in his country. Then they randomly select 64 SUVs whose mean price is $46,760. Assuming the standard deviation of the sample is 1370. Ida Lee conducts a hypothesis test to check their conclusion. At which significant level should Ida Lee reject the null hypothesis?

选项：

A.

0.5%.

B.

5%.

C.

1%.

解释：

B is correct.

If the significant level is 5%, the critical value=1.669<1.8978, Ida Lee should reject the null.

If the significant level is 0.5%, the critical value=2.656>1.8978, Ida Lee will fail to reject the null.

If the significant level is 1%, the critical value=2.387>1.8978, Ida Lee will fail to reject the null.


不是说下面的样本标准差要和上面的样本平均数对应吗？

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2 个答案

星星_品职助教 · 2022年05月18日

@Serein 好的，学习加油~

星星_品职助教 · 2022年05月17日

同学你好，

正是因为上面是 样本平均数 的均值，所以下面才应该匹配为 样本平均数 的标准差。而不应该是样本标准差。

根据中心极限定理，样本平均数的标准差=总体标准差σ/根号n，当σ未知时，用样本标准差s替代。

所以于样本平均数对应的标准差就是s/根号n

Serein · 2022年05月18日

谢谢老师！了解了！

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