Suppose you wish to detect a difference between 1 and 2 (either 1 > 2 or 1 < 2) and, instead of running a two-tailed

Suppose you wish to detect a difference between μ1 and μ2 (either μ1 > μ2 or μ1 < μ2) and, instead of running a two-tailed test using α = .05, you use the following test procedure. You wait until you have collected the sample data and have calculated 1 and 2. If 1 is larger than 2, you choose the alternative hypothesis Ha: μ1 > μ2 and run a one-tailed test placing α1 = .05 in the upper tail of the z distribution. If, on the other hand, 2 is larger than 1, you reverse the procedure and run a one-tailed test, placing α2 = .05 in the lower tail of the z distribution. If you use this procedure and if μ1 actually equals μ2, what is the probability α that you will conclude that μ1 is not equal to μ2 (i.e., what is the probability a that you will incorrectly reject H0 when H0 is true)? This exercise demonstrates why statistical tests should be formulated prior to observing the data.