Examples for Type I and Type II errors I was checking on Type I (reject a true H$_{0}$) and Type II (fail to reject a false H$_{0}$) errors during hypothesis testing and got to to know the definitions. But I was looking for where and how do these errors occur in real time scenarios. It would be great if someone came up with an example and explained the process where these errors occur.
 A: Let's say you are testing a new drug for some disease. In a test of its effectiveness, a type I error would be to say it has an effect when it does not; a type II error would be to say it has no effect when it does. 
A: Type I error /false positive: is same as rejecting the null when it is true. 
Few Examples: 


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*(With the null hypothesis that the person is innocent), convicting an innocent person

*(With the null hypothesis that e-mail is non-spam), non-spam mail is sent to spam box

*(With the null hypothesis that there is no metal present in passenger's bag), metal detector beeps (detects metal) for a bag with no metal


Type II error /false negative: is similar to accepting the null when it is false. 
Few Examples: 


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*(With the null hypothesis that the person is innocent), letting a guilty person go free.

*(With the null hypothesis that e-mail is non-spam), Spam mail is sent to Inbox

*(With the null hypothesis that there is no metal present in passenger's bag), metal detector fails to beep (does not detect metal) for a bag with metal in it
Other beautiful examples in layman's terms are give here:
Is there a way to remember the definitions of Type I and Type II Errors?
A: The boy who cried wolf.
I am not sure who is who in the fable but the basic idea is that the two types of errors (Type I and Type II) are timely ordered in the famous fable.
Type I: villagers (scientists) believe there is a wolf (effect in population), since the boy cried wolf, but in reality there is not any.
Type II: villagers (scientists) believe there is not any wolf (effect in population), although the boy cries wolf, and in reality there is a wolf.
Never been a fan of a examples that taught which one is "worse" as (in my opinion) it is dependent on a problem at hand.
A: A picture is worth a thousand words. Null hypothesis: patient is not pregnant.

Image via Paul Ellis.
A: Null hypothesis is: "Today is not my friends birthday."


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*Type I error: My friend does not have birthday today but I will wish her happy birthday.

*Type II error: My friend has birthday today but I don't wish her happy birthday.

