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eaglexps · 2022年03月23日

5%还是10% CI

  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.


老师我想问下，这道题是怎么判断出双尾的呢？因为如果是5%的CI的话，不应该是1，96码，但是我看题目写的是1.68，这个是10%的CI，那么就说明这是个双尾的。然而我看题目问的是看mean大于或小于，这个不是应该是one tail吗？谢谢

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2 个答案

星星_品职助教 · 2022年03月24日

@eaglexps

对的。总体方差未知，需要使用t分布。

本题并未给出总体的方差。这也是大部分的题目的情况。

星星_品职助教 · 2022年03月23日

同学你好，

1）本题为单尾检验；

2）本题为t分布，三个选项的critical value均为查t分布表得到的；

3）如果是正态分布，根据90%的置信区间对应关键值为1.65，可知单尾面积为5%时，关键值也为1.65；

4）和上一点做对比，在正态分布下，95%置信区间对应的关键值为1.96，即单尾面积为2.5%时关键值为1.96；

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