问题如下图：
选项：
A. 
B. 
C. 
解释：
老师，请问平时做题时，
X²0.05/2(24)=39.36和
X²1-0.05/2(24)=12.4
两个式子都要写出么？我觉得只需要其中一个就可以算出检验统计量X的值呀。
请指教
Danielle靓靓 · 2018年11月01日
老师您好。我查卡方分布表，N=25，拒绝域为5%，原假设区间概率为0.95时，卡方分布的值查出来是14.61呀，请问答案中12.4和39.6怎么来的呢？
菲菲_品职助教 · 2018年11月02日
要在自由度为24的卡方分布中，得到双侧概率为0.05所对应的上下端点可以这样来考虑：双侧概率指的是在上端和下端各划出概率相等的一部分，两概率之和为给定的概率值，这里是0.05，因此实际上上端点以上的概率为0.05/2=0.025，用概率0.025查表得上端点的值为39.36。下端点以下的概率也为0.025，因此可以用0.975查得下端点为12.4。
NO.PZ2015120604000144 问题如下 Quintina concts a hypothesis to test whether the varianof the annually return is 0.0144. Then she selects ranm 25 year's ta a sample, Quintina figures out the varianof the sample is 0.013924. Assume the level of significanis 5%, whiof the following conclusion is least accurate? A.The population varianis not significant fferent from 0.0144. B.The population varianis significantly fferent from 0.0144. C.This hypothesis is appropriate to use the chi-square test. B is correct. The null hypothesis is H0: σ2=0.0144. It is appropriate to use the two-tailechi-square test.The test statistic is:=(25-1)*0.013924/0.0144=23.21The criticchi-square criticvalues are 12.4 an39.36.Because the test statistic falls between these two values,so Quintina fails to rejethe null hypothesis. So we conclu ththe population varianis not significantly fferent from 0.0144.题干是问whiis the least accurate?所以选 如果在考试过程中也有类似的题，他会提供卡方的表吗？还是我们得自己记
NO.PZ2015120604000144 问题如下 Quintina concts a hypothesis to test whether the varianof the annually return is 0.0144. Then she selects ranm 25 year's ta a sample, Quintina figures out the varianof the sample is 0.013924. Assume the level of significanis 5%, whiof the following conclusion is least accurate? A.The population varianis not significant fferent from 0.0144. B.The population varianis significantly fferent from 0.0144. C.This hypothesis is appropriate to use the chi-square test. B is correct. The null hypothesis is H0: σ2=0.0144. It is appropriate to use the two-tailechi-square test.The test statistic is:=(25-1)*0.013924/0.0144=23.21The criticchi-square criticvalues are 12.4 an39.36.Because the test statistic falls between these two values,so Quintina fails to rejethe null hypothesis. So we conclu ththe population varianis not significantly fferent from 0.0144.题干是问whiis the least accurate?所以选 criticvalue 根据公式不应该是 24*23.21 吗？。criticvalue 地两个值如何算出来的？
NO.PZ2015120604000144问题如下 Quintina concts a hypothesis to test whether the varianof the annually return is 0.0144. Then she selects ranm 25 year's ta a sample, Quintina figures out the varianof the sample is 0.013924. Assume the level of significanis 5%, whiof the following conclusion is least accurate? A.The population varianis not significant fferent from 0.0144.B.The population varianis significantly fferent from 0.0144.C.This hypothesis is appropriate to use the chi-square test. B is correct. The null hypothesis is H0: σ2=0.0144. It is appropriate to use the two-tailechi-square test.The test statistic is:=(25-1)*0.013924/0.0144=23.21The criticchi-square criticvalues are 12.4 an39.36.Because the test statistic falls between these two values,so Quintina fails to rejethe null hypothesis. So we conclu ththe population varianis not significantly fferent from 0.0144.题干是问whiis the least accurate?所以选老师。。答案全出来了。。。用哪个值跟12.401和39比啊
NO.PZ2015120604000144 问题如下 Quintina concts a hypothesis to test whether the varianof the annually return is 0.0144. Then she selects ranm 25 year's ta a sample, Quintina figures out the varianof the sample is 0.013924. Assume the level of significanis 5%, whiof the following conclusion is least accurate? A.The population varianis not significant fferent from 0.0144. B.The population varianis significantly fferent from 0.0144. C.This hypothesis is appropriate to use the chi-square test. B is correct. The null hypothesis is H0: σ2=0.0144. It is appropriate to use the two-tailechi-square test.The test statistic is:=(25-1)*0.013924/0.0144=23.21The criticchi-square criticvalues are 12.4 an39.36.Because the test statistic falls between these two values,so Quintina fails to rejethe null hypothesis. So we conclu ththe population varianis not significantly fferent from 0.0144.题干是问whiis the least accurate?所以选 老师，这个原假设应该是H0:方差≠0.0144，还是=0.0144？因为他想要的=0.0144，所以要放在Ha=0.0144对吧。
NO.PZ2015120604000144 问题如下 Quintina concts a hypothesis to test whether the varianof the annually return is 0.0144. Then she selects ranm 25 year's ta a sample, Quintina figures out the varianof the sample is 0.013924. Assume the level of significanis 5%, whiof the following conclusion is least accurate? A.The population varianis not significant fferent from 0.0144. B.The population varianis significantly fferent from 0.0144. C.This hypothesis is appropriate to use the chi-square test. B is correct. The null hypothesis is H0: σ2=0.0144. It is appropriate to use the two-tailechi-square test.The test statistic is:=(25-1)*0.013924/0.0144=23.21The criticchi-square criticvalues are 12.4 an39.36.Because the test statistic falls between these two values,so Quintina fails to rejethe null hypothesis. So we conclu ththe population varianis not significantly fferent from 0.0144.题干是问whiis the least accurate?所以选 落在接受区域，接受原假设，即不能拒绝原假设，所以不是应该选A吗？