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sarahjia · 2020年03月01日

问一道题：NO.PZ2015120604000137

  1. CFA I
  2. Quantitative

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.


请问老师这道题为什么不查Z表呢，还有就是我看老师在其他提问里评论了C选项是”t统计量大于了这个临界值”可是C里1.8978不是比2.386这个临界值要小吗，

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星星_品职助教 · 2020年03月01日

同学你好，

这道题并没有说总体方差已知，且给了样本方差，所以从严格意义上来说，应该查t表。但这道题查Z表其实也不会影响结果，因为当N很大的时候，t会趋近于正态分布。所以从做题效率的角度，直接用背过的z值也是可以解题的。

但真实考试正常都会明示用哪个分布查哪个表的。

对于C选项，计算的t统计量值小于查表得到的tc，所以在1%的水平下，是不能拒绝原假设的。

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