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西红柿面 · 2023年10月09日

这题按道理来说应该是单尾检验吧？但是T分布图表没有告诉到底是单尾还是双尾的怎么办呢？

  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.


如题，这题按道理来说应该是单尾检验吧？但是T分布图表没有告诉到底是单尾还是双尾的怎么办呢？而且如果用Z分布代替的话应该怎么做呢？

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已采纳答案

星星_品职助教 · 2023年10月10日

同学你好，

本题为单尾检验。查T分布表的题目需要告知是单尾t表还是双尾t表，或至少给出可以判断的条件。否则无法查表。

由于教材给的t分布表为单尾t表，除了几道较老的Mock题外，目前绝大多数的题目都是基于单尾t表来查表的。

z分布需要根据significance level来判定关键值。例如significance level=5%且为单尾检验，说明单尾的面积就是5%。这就对应着要求背诵的那一组关键值中的1.65。

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