Upper and Lower Bounds for Confidence Intervals on a one tail hypothesis test.

Question

CI(99) = xbar ± Zcv( σ / √ n -1 )

My question is if the test is a one tail hypothesis test, do I still do two separate equations + and -.

Here is the formula filled in (if it is the correct formula) CI(99) = xbar ± (-2.33? or |2.33|)(.56 / √86-1)

Answer 1

If you want a one-sided confidence interval, then you need to adjust your Z-score such that the probability above that Z-score (for upper-tail tests, lower CI) or below that Z-score (for lower-tail tests, upper CI) is equal to your significance level.

For example, a 1-sided, lower confidence interval is: $-\infty $ to $\bar x + z_{1-\alpha}\frac{\sigma}{\sqrt{n}}$, while the upper confidence interval is $\bar x - z_{1-\alpha}\frac{\sigma}{\sqrt{n}}$ to $\infty$

BTW: If you're using a z-test, then you are assuming you know the variance, and hence you don't need to divide by n-1, just n. The n-1 is only used in estimating an unbiased sample variance - note: the square root of the unbiased varince estimator is not unbiased, but biased low...the correction for this is tedious and often unnecessary if your sample size is greater than a handful of points.