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许晏宁 · 2022年10月08日

No.PZ2022071202000085 (选择题)

NO.PZ2022071202000085

问题如下:

Question A small-cap growth fund’s monthly returns for the past 36 months have been consistently outperforming its benchmark. An analyst is determining whether the standard deviation of monthly returns is greater than 6%. Which of the following best describes the hypothesis to be tested?

选项:

A.H0: σ2 ≤ 0.36% B.Ha: σ2 > 6% C.H0: σ2 ≥ 0.36%

解释:

Solution

A is correct. This is a one-tailed hypothesis testing with a “greater than” alternative hypothesis. A squared standard deviation is being used to obtain a test of variance. The hypotheses are H0: σ2 ≤ 0.36% versus Ha: σ2 > 0.36%.

B is incorrect as explained in choice A.

C is incorrect as explained in choice A

这里的0.36%是怎么来的

2 个答案

星星_品职助教 · 2022年10月09日

@许晏宁

题干要求检验的是“whether the standard deviation of monthly returns is greater than 6%”,

由于没有直接针对standard deviation的检验,所以只能将其平方,转化为方差的卡方检验。

即此时就转化成了检验方差是否等于一个确定的数字0.36%

星星_品职助教 · 2022年10月08日

同学你好,

题干描述的是standard deviation即标准差是否大于6%,而卡方检验针对的是方差。

所以需要将standard deviation转化为方差后再检验,即将6%平方后得到0.36%。

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