问题如下:
Quintina conducts a hypothesis to test whether the variance of the annually return is 0.0144. Then she selects a random 25 year's data as a sample, Quintina figures out the variance of the sample is 0.013924.Assume the level of significance is 5%, which of the following conclusion is least accurate?
选项:
A.The population variance is not significant different from 0.0144.
B.The population and sample variances are significantly different.
C.This hypothesis is appropriate to use the chi-square test.
解释:
B is correct.
The null hypothesis is H0: σ2=0.0144. It is appropriate to use the two-tailed chi-square test.
The test statistic is:
The critical chi-square critical values are 12.4 and 39.36.
Because the test statistic falls between these two values,so Quintina fails to reject the null hypothesis.
So we conclude that the population variance is not significantly different from 0.0144.
chi-squared distribution only has one-tailed. 所以为什么不是直接找到df=24, prob=0.05 对应的 entry 36.42, 然后用test statistic 和36.42 比大小就好?