9.21 Suppose you wish to detect a difference between and (either or ) and, instead of running a two-tailed test using a = 0.05, you use the following test procedure. You wait until you have collected the sample data and have calculated and 2. If x, is larger than 2, you choose the alternative hypothesis H, and run a one-tailed test placing a 0.05 in the upper tail of the z distribution. If, on the other hand, is larger than 1, you reverse the procedure and run a one-tailed test, placing a =0.05 in the lower tail of the z distribution. If you use this procedure and if , actually equals , what is the probability a that you will conclude that , is not equal to (i.e., what is the probability & that you will incorrectly reject Ho when Ho is true)? This exercise demonstrates why statistical tests should be formulated prior to observing the data.