Ⅷ Types of error State of realit Ho True Ho False ype Test True 0 No error error Says TYp e l error No error False o 2002 The Wadsworth Group
Types of Error No error Type II error: b Type I error: a No error State of Reality H0 True H0 False H0 True H0 False Test Says © 2002 The Wadsworth Group
l Types of error ype I error Saying you reject Ho when it really is true Rejecting a true Ho ° Type I error: saying you do not reject ho when it really is false Failing to reject a false h o 2002 The Wadsworth Group
Types of Error • Type I Error: – Saying you reject H0 when it really is true. – Rejecting a true H0 . • Type II Error: – Saying you do not reject H0 when it really is false. – Failing to reject a false H0 . © 2002 The Wadsworth Group
I Acceptable Error for the example Decision makers frequently use a 570 significance level -Usea=0.05 An a-error means that we will decide to adjust the machine when it does not need adjustment This means, in the case of the robot welder if the machine is running properly, there is only a 0.05 probability of our making the mistake of concluding that the robot requires adjustment when it really does not o 2002 The Wadsworth Group
Acceptable Error for the Example • Decision makers frequently use a 5% significance level. – Use a = 0.05. – An a-error means that we will decide to adjust the machine when it does not need adjustment. – This means, in the case of the robot welder, if the machine is running properly, there is only a 0.05 probability of our making the mistake of concluding that the robot requires adjustment when it really does not. © 2002 The Wadsworth Group
l The Null Hypothesis Nondirectional, two-tail test Ho: pop parameter = value Directional, right-tail test 0: pop parameter< value Directional, left -tail test. pop parameter z value Always put hypotheses in terms of population parameters. Ho always gets o 2002 The Wadsworth Group
The Null Hypothesis • Nondirectional, two-tail test: – H0 : pop parameter = value • Directional, right-tail test: – H0 : pop parameter value • Directional, left-tail test: – H0 : pop parameter value Always put hypotheses in terms of population parameters. H0 always gets “=“. © 2002 The Wadsworth Group
I Nondirectional, Two-Tail tests Ho pop parameter=value H1: pop parameter value Do Not Reject H Reject H Reject H 0 0 2 杬 Z o 2002 The Wadsworth Group
Nondirectional, Two-Tail Tests H0 : pop parameter = value H1 : pop parameter value a −a a 杬 +z Do Not Reject H 0 Reject H 0 Reject H 0 © 2002 The Wadsworth Group