Self Study Question:
We already know that the confidence interval of a parameter M is (-1,2). We are supposed to find the confidence interval of 1/M. The function is 1/X, which is One to One, so ideally we are just supposed to plug in the endpoint values into the function, but this doesn't seem right in my head.
P(-1 <= M <= 2) = .9, but 1/X is monotonic above and below x = 0, but they are not the same monotonic "direction" (for x<0, f'(x) < 0, and for x>0, f'(x) > 0 for all points x).
It wouldn't make sense to apply 1/x to an inequality and expect it to hold since it does not preserve the order of values that cross x = 0. Can someone tell me if my logic is wrong, or if I am right, how to proceed with this question? Thanks.