16. Suppose you wish to detect a difference between m1 and m2 (either m1 . m2 or m1 , m2) and, instead of running a two-tailed test using a 5 .05, you use the following test procedure. You wait until you have collected the sample data and have calculated 1 x and 2 x . If 1 x is larger than 2 x , you choose the alternative hypothesis

: > a 1 2 H m m and run a one-tailed test placing a1 5 .05 in the upper tail of the z distribution. If, on the other hand, 2 x is larger than 1 x , you reverse the procedure and run a one-tailed test, placing a2 5 .05 in the lower tail of the z distribution. If you use this procedure and if m1 actually equals m2, 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.