Let

Let X1, , X" be i.i.d. Bernoulli random variables with unknown parameter p E (0, 1) . Suppose we want to test 3.3 :pE [043,051] vs 111 2\"; [043,051] We want to construct an asymptotic test 1;! for these hypotheses using 317,. . For this problem, we specifically consider the family of tests we\": wherewe reject the null hypothesis if either 3?... c; z 0.5] for some cl and c; that may depend on n, i.e. Wow: = 1 ((17,, cg) where (:1 c2). on each of the three cases for the value ofp in terms of (:1, (:2, and n, and determine in each case which component(s) of the Type 1 error will converge to zero. This would allow you to come up with a new set of conditions for CI and (:2 in terms of it, given the desired level of 5%. Enter these values (in terms of n) below. (If applicable, enter qtalpha) for q", the 1 a -qua ntile of a standard normal distribution, e.g. enter q(0.01) for qom . Do not worry about the parser not rendering q(alpha) properly; the grader will work nonetheless. You could also enclose qtalpha) by brackets for the rendering to show properly} cl .9 ll