Consider a six faced die whose i-th face is marked with z dots, i = 1, 2,...,6. In a single random throw of the die, let p_i denote the probability that the obtained upper face has i dots, i = 1, 2,...,6. The die is rolled 240 times independently and the following result is obtained 

Face observed	1	2	3	4	5	6
Frequency	40	55	40	25	35	45

Suppose we want to test H₀ : \(\rm p_i=\frac{1}{6}\) for i = 1, 2,...,6; against H₁ : p_i ≠ \(\frac{1}{6}\) for at least one i;i = 1, 2,...,6. It is given that \(\rm χ_{5; 0.05}^2\) = 11.07, \(\rm χ_{6; 0.05}^2\) = 12.59, \(\rm χ_{5; 0.01}^2\) = 15.09, \(\rm χ_{6; 0.01}^2\) = 16.81. Based on the asymptotic goodness of fit χ² test for testing H₀ against H₁, which of the following statements are true?