More details on the lecture example:
Null hypothesis: Carpeting is fine and does not cause any infections. Alternative hypothesis: Having carpeting results in infections.
Which is worse — option 1: assuming the carpeting is fine and doing nothing, but really everyone is getting really sick?
- This is a type II error
- If this option is worse, you want a larger significance level, maybe 0.10
- A significance level of 0.10 means you are comfortable with a 10% chance of incorrectly rejecting the null hypothesis
- You’d rather make sure you re-carpet if there’s even a medium chance that it could be causing infection
OR option 2: is it worse to pay to re-carpet the hospital but really the carpet was totally fine?
- This is a type I error
- If this option is worse, you want a smaller significance level, maybe 0.01
- A significance level of 0.01 means you are comfortable with a 1% chance of incorrectly rejecting the null hypothesis
- You only want to pay to re-carpet if you’re really, really sure that it’s a problem.