Sunday, May 30, 2010

Statistical Hyposthesis Testing

In hypothesis Testing, there are two hypotheses. The first one is called null hypothesis H0, which usually the hypothesis we would like to test. The second one is called alternative hypothesis H1. When we reject H0, the leads to accepting H1.

Technically, H0 is something we hope if we make wrong decision, it will have less severe effects. For example, in a murder case, a suspect is put in a trial. The judge could have two ways of thinking.

H0: The suspect is the murderer.
H1: The suspect is innocent.

or
H0: The suspect is innocent.
H1: The suspect is the murderer.

Can you guess which one every judge think?  Of course, the later one. By assume that the suspect is innocent (but he is not), the judge may let go of the suspect (wrong decision). If the judge makes wrong decision, no one die more in the process. However, in the first thinking, The judge may put an innocent people to be killed.

In product inspection for manufacturing process, H0 is the assumption that the product is good, H1 is the otherwise.

Why?, well try to think in terms of the cost of inspection from the manufacturer's point of view.

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