Hello, could you help solve this problem step by step with well-formatted formulas? Hand written answers are also welcome!

Suppose X1,X2,...,X100 is a random sample fromN(0,2) with unknown variance 2, and letYi=I{Xi>1.96}, i=1,...,100, where I is indicator function equaling 1 if the absolute value ofXi is greater than 1.96 and 0 otherwise. Consider testingH0:2=1 versusH1:2=1.

(a). Construct a 0.05 level test for the above hypotheses based on Xi, i=1,...,100 ?

(b). Construct a 0.05 level test for the above hypotheses based on Yi,i=1,...,100