Cond. Heteroskedasticity test with BP

CFA text on Quant , Pg370 Problem 11 Why is the Chi-Square test done at the 0.05 level of significance whereas the main regression is done at 0.01 level? This fooled me totally. The answers are different if you read the Chi-Sq tables for 0.01 level . The nR^2 value is 4.5 From Chi-sq tables for 1 degree of freedom: 3.841 : at the 0.05 level of significance : Reject the null , correct for cond. heteoskedasticity 6.635 : at the 0.01 level of significance : Do NOT Reject the null , no need to correct. Philosophically , the stricter the test , the more likelihood of failure , so I basically don’t get that the test passes at a stricter level of significance and fails for a looser level Please , if anybody got this right , give me some hints!

I don’t believe that there’s any need to tie in the two tests together. Meaning that you have to be at the same level of confidence for both of them.