Suppose you wish to detect a difference betweenm1 and m2 (either m1 m2 or m1 m2) and

Chapter 9, Problem 20

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Suppose you wish to detect a difference betweenm1 and m2 (either m1 m2 or m1 m2) and, instead ofrunning a two-tailed test using a .05, you use thefollowing test procedure. You wait until you have collectedthe sample data and have calculated x1 and x2.If x1 is larger than x2, you choose the alternativehypothesis Ha : m1 m2 and run a one-tailed test placinga1 .05 in the upper tail of the z distribution. If,on the other hand, x2 is larger than x1, you reverse theprocedure and run a one-tailed test, placing a2 .05in the lower tail of the z distribution. If you use thisprocedure and if m1 actually equals m2, what is theprobability a that you will conclude that m1 is notequal to m2 (i.e., what is the probability a that you willincorrectly reject H0 when H0 is true)? This exercisedemonstrates why statistical tests should be formulatedprior to observing the data.