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南极耳语 · 2021年02月22日

老师请附一下这道题完整的解题过程

  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.


老师请写一下完整的解题过程感谢

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2 个答案

星星_品职助教 · 2021年04月18日

@颇具才干的小灰灰

题干中说明“ the standard deviation of the sample is 1370”，所以这是样本标准差的概念，并非总体标准差/方差已知。正是因为总体标准差未知，才需要用样本标准差去代替总体标准差

星星_品职助教 · 2021年02月23日

同学你好，

本题问是否拒绝原假设。所以需要对比|t-statistics|和|t critical value|的（绝对值的）大小（如果|t-statistics|＞|t critical value|，则此时拒绝原假设）。

t-statistics的计算如下：

(46760-46435)/(1370/√64)=1.8978

逐个查表得到0.5%，5%，1% significant level下各自的t critical value。然后将绝对值分别和1.8978进行对比。

发现只有当significant level=5%时，t critical value=1.669＜1.8978，所以可以拒绝原假设。

---------------------

建议提问时具体说一下哪个点不懂，问题是什么（e.g.答案解析某个点不明白/题干某句话看不懂/选项里的某个知识点遗忘等）

不然助教不知道重点应该去强调哪个方面的。

颇具才干的小灰灰 · 2021年04月18日

为什么用t检验而不是z？题目中已知standard deviation，就相当于已知方差。

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