Type I and II, HO and H1

#1
I am committing to memory the definitions of the Type I and II error rates, but my brain is having difficulty when looking at a null and alternative hypothesis in light of those. For example, if I am asked to write in "plain" english what a Type I error or Type II error rate would be in context of an experiment, I look to each the null and alternative and write 2 statements.

The major confusion lies when I am reading failing to reject or rejecting the null....the failing to reject makes me think accept the null, but it gets messy when I think it out. For example:

Ho: reduced classroom size is not effective
H1: reduced classroom size is effective

A. Explain in plain english what the type I error rate would be in the context of this experiment.
B. Explain in plain english what the type II error rate would be in the context of this experiment.

Type I error is the probablility of falsely rejecting the null
Type II is failing to reject the null when the null is true

How do I know where to put in my answer - in a statement about the null or alternative?

Are my working definitions of type I and II right? Any good ways to think about answering this question? Thanks!
 

JohnM

TS Contributor
#2
Your Type I error statement is correct:
Type I error is the probablility of falsely rejecting the null

but Type II error should be:
Type II is failing to reject the null when the null is false

Ho: reduced classroom size is not effective
H1: reduced classroom size is effective

Without knowing any other info, I'm assuming that this experiment or study compares "large" or "standard-size" classrooms to "reduced-size" classrooms, and some measure of student learning will be used as the basis of comparison...

The questions are worded a bit strangely, in that they ask about the error "rate" - it should just refer to error
A. Explain in plain english what the type I error rate would be in the context of this experiment
Concluding that a reduced classroom size is effective, when in reality it is not.

B. Explain in plain english what the type II error rate would be in the context of this experiment
Concluding that a reduced classroom size is not effective, when in reality it is effective.