P-Value Statistics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

hard
A test gives a p-value of 0.12. Interpret this and state the decision at ฮฑ=0.05\alpha = 0.05.

Solution

  1. 1
    Step 1: p=0.12>0.05=ฮฑp = 0.12 > 0.05 = \alpha.
  2. 2
    Step 2: We fail to reject H0H_0. The data does not provide sufficient evidence against the null hypothesis.
  3. 3
    Step 3: Note: 'fail to reject' is not the same as 'accept'. We simply lack strong enough evidence.

Answer

Fail to reject H0H_0. Insufficient evidence at the 0.05 level.
A large p-value means the observed data is reasonably likely under H0H_0. We say 'fail to reject' rather than 'accept' because absence of evidence is not evidence of absence.

About P-Value

The p-value is the probability of observing results at least as extreme as the actual data, calculated under the assumption that the null hypothesis is true. A small p-value (typically below 0.05) suggests the observed data is unlikely under the null, providing evidence against it.

Learn more about P-Value โ†’

More P-Value Examples

Example 1 hard

A two-tailed z-test gives [formula]. The p-value is approximately 0.008. If [formula], should we rej

Example 3 hard

A researcher obtains [formula]. Would the result be significant at [formula]? At [formula]?

Example 4 hard

A hypothesis test gives a p-value of 0.20. What decision would you make at [formula] and at [formula

โ† All P-Value Examples P-Value Concept