Statistic Question for Econometrics

Question

Hi! I am working on an econometrics midterm review, and I had a question. If I have to do a mean left tail hypothesis testing and build the confidence interval at 95%, would the confidence interval still be: "X bar -+ 1.96 SE(x)", or would it be only one side, and if it would be only one side would I have to change the 1.96 to 1.64?

Answer 1

If you are testing:

Ho: u=uo (or u>= uo)

vs H1: u<uo

where u= population mean, uo= constant

and you want to build a one-sided 95% Confidence interval,

then you don't have to divide ∝ by 2. So use 1.64 (or 1.645) -- make sure you use the appropriate critical value (could be z or t)

The CI will be:

(-∞ , Xbar - 1.645*SE(Xbar) )

HTH