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许晏宁 · 2022年10月09日

No.PZ2022071202000102 (选择题)

NO.PZ2022071202000102

问题如下:

Question During the past 36 months, the standard deviation of a portfolio’s monthly returns has been 4.9%. To test a claim that this portfolio’s investment strategy results in a standard deviation of monthly returns that is less than 5.0%, the value of the test statistic is closest to:

选项:

A.34.30. B.33.61. C.34.57.

解释:

Solution

B is correct. The most appropriate test is chi-square, with 36 -1 = 35 degrees of freedom. The calculated test statistic is: where

χ2 = is the chi-square test statistic

n = is the sample size

s2 = is the sample variance

σ 0 2 = the hypothesized value of the variance σ2

A is incorrect. If there is no squared to both s and σ.

36?1 0.049 0.05 =34.30

C is incorrect. If using n as degrees of freedom instead of n - 1, that is

36 0.049 2 0.05 2 =34.57

麻烦老师带数计算一下,总是算不出来答案里的结果

1 个答案

星星_品职助教 · 2022年10月09日

同学你好,

1)standard deviation=4.9%,所以s的平方为0.2401%。

2)n=36,所以n-1=35

3)由于检验的是“...standard deviation... less than 5.0%”,所以σo=5%。

将上述三者代入公式:

得到卡方统计量为:35×0.2401% / 5%的平方=33.6140,即选择B选项

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