题目
A new equity fund called Machine Trade Bet is managed by an artificially intelligent bot who utilizes machine learning. The fund claims that its true (population) volatility does not exceed 15.0% per annum. However, based on a random sample of 40 observations, a sample volatility of 17.0% per annum is calculated. The desired confidence level is 95.0%; further this is a one-side test as the null hypothesis assumes the volatility is equal to, or less than, 15.0% per annum. Should the null hypothesis be rejected, in favor of the alternative hypothesis which asserts that the fund's true volatility exceeds 15.0%?
选项
A.No, because the test statistic of 50.09 is less than the critical value of 54.57
B.No, because the test statistic of 44.20 is less than the critical value of 55.76
C.Yes, because the test statistic of 45.33 is less than the critical value of 58.12
D.Yes, because the test statistic of 51.38 is less than the critical value of 59.34
答案
A
解析
No, because the test statistic of 50.09 is less than the critical value of 54.57.This is a test of the sample variance such that the test statistic is equal to「huixue_img/importSubject/1564169386795864064.png」 The critical value at one-tailed 95.0% is given by 54.57; i.e., at 39 degrees of freedom, the Prob「huixue_img/importSubject/1564169386837807104.png」.Equivalently , CHISQ.INV(0.950,39) = 54.57. Consequently, we cannot reject the null: the true volatility might be 15.0% or less. Compare, just for example, to a scenario where we might observe the same difference (17.0% versus 15.0%) but with 100 observations;in this case, the test statistic of「huixue_img/importSubject/1564169386871361536.png」 would exceed the critical value of CHISQ.INV(0.950,99) = 123.23, and the null would be rejected.