Writing Null and Alternative Hypotheses: Symbols and Decisions

All flashcards

What is the null hypothesis?

The null hypothesis, $H_0$, is a claim about a population that commonly represents no difference, no relationship, or the status quo. It is assessed using sample evidence.

What is the alternative hypothesis?

The alternative hypothesis, $H_a$, is the claim that contradicts $H_0$. It often expresses what the researcher is investigating and is favored when evidence is strong enough to reject the null.

What symbol rule distinguishes $H_0$ from $H_a$?

$H_0$ includes equality, using $=$, $\leq$, or $\geq$. $H_a$ excludes equality, using $\neq$, $<$, or $>$.

How do you write hypotheses for a claim that a proportion is more than 30%?

Place the claim in the alternative: $H_a: p > 0.30$. The complementary null is $H_0: p \leq 0.30$.

What does “do not reject $H_0$” mean?

The sample evidence did not meet the chosen standard for rejecting the null. It does not prove that $H_0$ is true.

Quiz questions

1. Which kind of symbol does a null hypothesis include by convention?Answer: Equality, such as $=$, $\leq$, or $\geq$.
2. A researcher tests whether more than 40% of a population has a characteristic. Which hypotheses fit that claim?Answer: $H_0: p \leq 0.40$ and $H_a: p > 0.40$
3. A researcher asks whether a population mean differs from 12. Which alternative hypothesis matches the question?Answer: $H_a: \mu \neq 12$
4. What does an analyst examine to assess whether there is evidence against the null hypothesis?Answer: Sample data from the population of interest.