Statistics / Unit 9: Hypothesis Testing Basics
9.1 Null and Alternative Hypotheses
Notes
A hypothesis test uses sample data to decide between two competing claims about a population parameter.
- The null hypothesis $H_0$ is the claim of "no effect" or "no change." It always states equality, such as $p = 0.5$ or $\mu = 70$.
- The alternative hypothesis $H_a$ is what we suspect or hope to find evidence for. It uses $<$, $>$ or $\ne$.
- Hypotheses are about parameters ($p$, $\mu$), never statistics ($\hat{p}$, $\bar{x}$).
- Example: A company claims $90\%$ of packages arrive on time, and a customer group thinks it is lower: $H_0: p = 0.9$ and $H_a: p < 0.9$.
Practice
A company claims that $90\%$ of its packages arrive on time. A customer group suspects the true percent is lower. The hypotheses are:
The null states equality, the alternative matches the suspicion (lower), and both are about the parameter $p$.
Which is a properly stated null hypothesis?
A null hypothesis is an equality about a population parameter.
A researcher believes a new teaching method raises the mean score above 70. The alternative hypothesis is:
The researcher expects an increase, so $H_a$ is $\mu > 70$.
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