ch16NormaltestofHypothesesonmu0.studentview

ch16NormaltestofHypothesesonmu0.studentview - Chapter 16 :...

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Unformatted text preview: Chapter 16 : Normal Test of Hypotheses on A. General Concepts When we carry out a research project or experiment, we may have reservations about the validity of certain existing theories, or facts, or beliefs. We then collect data in the hope of establishing a new theory, presented in the form of a hypothesis (statement). There are thus two hypotheses for us to decide between: The old, existing and authoritative one is called the null hypothesis , denoted by H The new, daring or challenging one is called the alternative hypothesis , denoted as They are not of equal standing. The old one, , is in a privileged position, as it has been established and used for some time, perhaps for centuries. The new one, , is fragile. It is essentially a trouble maker. People would not mind giving it up if evidence is not strong enough to support it. This is in accord with some western legal points of view. 1 H H A = A H H In a court case, the prosecutor (or the plaintiff) proposes an hypothesis: :Mr A. has committed a crime, X The judge in the first place already assumes an hypothesis : Mr A. is innocent of X. This is proposed to nullify (to validate) . The trial (i.e. the test) then goes on. The verdict might turn out to be or . H A H A H A H H H There are two types of errors : Correspondingly, there are two types of risks in the test: = Type I risk = P ( Commit Type I error) = Type II risk = P( Commit Type II error) Ideally, the trial procedure (i.e. the test) can be designed so that both and are small. If however, the judge cannot keep both and small, then he chooses to give up . He, in the first place, must keep as small as possible, so as to protect the defendants rights. In other words, the court does not want to wrong an innocent person. Thus, the focus is on the control of . Usually, the choice of the -value depends on the nature of X. (i) If X = illegal parking, then perhaps, = 0.05 (ii) If X = speeding, then perhaps,= 0.01 (iii) If X = murdering, then = 0.001, or less....
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ch16NormaltestofHypothesesonmu0.studentview - Chapter 16 :...

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