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Example 1 - Courtroom trial

Example 1 - Courtroom trial A statistical test procedure is comparable to a trial ; a defendant is considered not guilty as long as his guilt is not proven. The prosecutor tries to prove the guilt of the defendant. Only when there is enough charging evidence the defendant is convicted.

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Example 1 - Courtroom trial

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  1. Example 1 - Courtroom trial A statistical test procedure is comparable to a trial; a defendant is considered not guilty as long as his guilt is not proven. The prosecutor tries to prove the guilt of the defendant. Only when there is enough charging evidence the defendant is convicted. In the start of the procedure, there are two hypotheses H0: "the defendant is not guilty", and H1: "the defendant is guilty". The first one is called null hypothesis, and is for the time being accepted. The second one is called alternative (hypothesis). It is the hypothesis one tries to prove. The hypothesis of innocence is only rejected when an error is very unlikely, because one doesn't want to convict an innocent defendant. Such an error is called error of the first kind (i.e. the conviction of an innocent person), and the occurrence of this error is controlled to be rare. As a consequence of this asymmetric behaviour, the error of the second kind (acquitting a person who committed the crime), is often rather large.

  2. Hipotézis tesztelés Null hipotézis (H0). Elfogadjuk, ha nem bizonyul hamisnak Alternatív hipotézis (Ha): Elmélet, amely ellentétben áll a Null hipotézissel. Teszt statisztika Rejekciós régió: A teszt statisztika azon értéke, amely mellett elvetjük a Null hipotézist (alfa) Feltételezések Kísérlet, a teszt statisztika számítása Következtetés: a) Ha a teszt statisztika értéke a rejekciós területre esik, elvetjük a Null hipotézist és elfogadjuk az alternatív hipotézist. I-es típusu hiba valószínüsége: 100*alfa%. b) Ha a teszt statisztika értéke nem esik a rejekciós területre, nem vetjük el a Null hipotézist (De nem vetjük el az alternatív hipotézist sem!). II-s típusu hiba valószínüsége nem ismert!

  3. Null és alternatív hipotézis kiválasztása • Példa: • H0: átlag=2400 • Ha: • A) Egy oldalú: átlag > 2400 • B) Egy oldalú: átlag < 2400 • C) Kétoldalú : átlag <>2400

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