Every Statistic Hypothesis involves two opposite statements about a population parameter (like ).
Concepts
Null hypothesis (Ho):
The “status quo” or a statement of no effect / no difference.
- Usually contains an equality: .
- We assume it is true unless sample evidence strongly contradicts it.
Alternative hypothesis, denoted (or Ha):
The opposite of , what we suspect or want to prove.
- Contains a strict inequality: .
- Key rule: is always stated first, then .
Examples from the text:
- Suspect that the illiteracy rate in Peru is at most 5%:
- Suspect the average exam score is below 13:
How to Formulate
Often it is easier to identify first (what you want to prove), then is simply the opposite.
Two common scenarios
H_a as the research hypothesis
When you want to demonstrate that something is better, more effective, higher, etc.
- states the improvement; states “no improvement” or “not better.”
Example: A new teaching method is believed to be better than the current one.
- : The new method is not better.
- : The new method is better.
Ho as an assumption to be challenged
Often used in quality control or label verification.
- contains the claimed or required value (with , , or ).
- is the opposite (e.g., under‑filling, over‑filling, not meeting specification).\
Example: A soda bottle label says 0.5 L
- (the claim is correct)
- (the claim is false)