No.PZ2022071202000102 (选择题)

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

${\sigma }_0^2$ = the hypothesized value of the variance σ²

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

$\frac{\left(36?1\right)\left(0.049\right)}{\left(0.05\right)}=34.30$

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

$\frac{\left(36\right){\left(0.049\right)}^2}{{\left(0.05\right)}^2}=34.57$