There are two hypotheses, both of which are equally likely:

H0: X~ N(1,1)

H1: X ~ N(2,4)

Given a single sample ofX=x,determine a decision ruleto determine which of hypothesis H0orH1 occurred. Use themaximum likelihoodrule.

The possible decision regions listed below correspond to the decision region forH0, meaning that the optimal ML rule decides that the hypothesis isH0if the observed samplexlies in the interval below.

answer choices:

(-.84, 2.18)

(0,1.5)

(0,2)

(-inf, 1.5)

(-inf, 1.25)

(-2,2)