Thread: Type II Error Question

You have made a type II error. Which statement is correct

1The alternative hypothesis is false, and you rejected the null
2.The alternative hypothesis is true, and you rejected the null
3.The alternative hypothesis is false, and you did not reject the null
4.The alternative hypothesis is true, and you did not reject the null
5.None of these are correct

A type II error in hypothesis testing describes the event of accepting a null hypothesis that is actually false.

Originally Posted by pickslides

A type II error in hypothesis testing describes the event of accepting a null hypothesis that is actually false.

Thus, 3 is correct then?

Of the options 1-4, option 4 seems the most correct, logically speaking.

Originally Posted by mrcode

4.The alternative hypothesis is true, and you did not reject the null

I was always taught not to use the terminology "The alternative hypothesis is true", its best just to say their is evidence to suggest the null hypothesis should be rejected, and you failed to reject it. So on terminology alone I would pick option 5.

Pickslides,

You're really confusing me here. Is 4 really not right? And if so, why is 5 right?

Originally Posted by pickslides

Of the options 1-4, option 4 seems the most correct, logically speaking.



I was always taught not to use the terminology "The alternative hypothesis is true", its best just to say their is evidence to suggest the null hypothesis should be rejected, and you failed to reject it. So on terminology alone I would pick option 5.

If terminology is an issue here I would pick 5, although that is me splitting hairs.

Option 4 seems logically correct.

It is 4, and terminology isn't an issue IMO. Assuming the model is correct, the alternative is either true or false; a type II error is failing to reject the null hypothesis when the alternative is true.

What people typically have a problem with, terminology wise, is saying "I accept the null hypothesis" or similar statements. In a decision-theoretic context the distinction is meaningless, so I tend not to split hairs, although some instructors (typically introductory-level stat teachers) can be incredibly anal about these things.

4

We seem to be converging on 4.