Math / Data & Statistics

QuestionWhich of the given sentences about stating hypotheses is true? Both $H_{a}$ or $H_{0}$ could contain the equality. $H_{a}$ can contain the equality. $H_{0}$ always contains the equality.

Studdy Solution

STEP 1

1. $H_0$ represents the null hypothesis.
2. $H_a$ represents the alternative hypothesis.
3. The null hypothesis typically includes the equality.

STEP 2

1. Define the characteristics of $H_0$ .
2. Define the characteristics of $H_a$ .
3. Evaluate each given sentence based on the definitions.

STEP 3

The null hypothesis $H_0$ is a statement of no effect or no difference and typically includes the equality sign. For example, $H_0: \mu = \mu_0$ .

STEP 4

The alternative hypothesis $H_a$ is a statement that indicates the presence of an effect or difference and typically does not include the equality sign. For example, $H_a: \mu \neq \mu_0$ , $H_a: \mu > \mu_0$ , or $H_a: \mu < \mu_0$ .

STEP 5

Evaluate each sentence:
- "Both $H_{a}$ or $H_{0}$ could contain the equality." - This is false because typically only $H_0$ contains the equality.
- " $H_{a}$ can contain the equality." - This is false because $H_a$ typically does not contain the equality.
- " $H_{0}$ always contains the equality." - This is true because $H_0$ is usually stated with an equality.
The true sentence is:
$\boxed{H_{0} \text{ always contains the equality.}}$

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