P-Value Statistics Example 4

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

Example 4

hard
A hypothesis test gives a p-value of 0.20. What decision would you make at α=0.10\alpha = 0.10 and at α=0.05\alpha = 0.05?

Solution

  1. 1
    Step 1: Because 0.20>0.100.20 > 0.10, the result is not significant at α=0.10\alpha = 0.10, so we fail to reject H0H_0.
  2. 2
    Step 2: Because 0.20>0.050.20 > 0.05 as well, we also fail to reject H0H_0 at α=0.05\alpha = 0.05.

Answer

Fail to reject H0H_0 at both α=0.10\alpha = 0.10 and α=0.05\alpha = 0.05.
A p-value must be smaller than the chosen alpha level to count as statistically significant. A p-value of 0.20 is too large for either of these common significance levels.

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 →

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 2 hard

A test gives a p-value of 0.12. Interpret this and state the decision at [formula].

Example 3 hard

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

← All P-Value Examples P-Value Concept