Let X be a random variable whose probability mass functions under H0 and H1 are given by the following
\(\begin{array}{rccccccc} x & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline f_{H_0}(x) & 0.01 & 0.01 & 0.01 & 0.01 & 0.01 & 0.01 & 0.94 \\ f_{H_1}(x) & 0.06 & 0.05 & 0.04 & 0.03 & 0.02 & 0.01 & 0.79 \end{array}\)
where, \(f_{H_0}(x)=P_{H_0}(X=x) \) and \(f_{H_1}(x)=P_{H_1}(X=x)\). Which of the following statements are correct?
1
The critical region of most powerful test of size α = 0.04, for testing H0 against H1, is given by {x : x ≤ 4}
2
The critical region of most powerful test of size α = 0.04, for testing H0 against H1, is given by {x : 3 ≤ x ≤ 6}
3
The power of the most powerful test of size α = 0.04, for testing H0 against H1, is 0.18
4
Most powerful test of size α = 0.04, for testing H0 against H1, does not exist