P-Value Statistics Example 3

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

Example 3

hard
A researcher obtains p=0.03p = 0.03. Would the result be significant at α=0.05\alpha = 0.05? At α=0.01\alpha = 0.01?

Solution

  1. 1
    Step 1: At α=0.05\alpha = 0.05: 0.03<0.050.03 < 0.05 → reject H0H_0 (significant).
  2. 2
    Step 2: At α=0.01\alpha = 0.01: 0.03>0.010.03 > 0.01 → fail to reject H0H_0 (not significant).

Answer

Significant at α=0.05\alpha = 0.05 but not at α=0.01\alpha = 0.01.
The choice of significance level affects the conclusion. A stricter (smaller) α\alpha requires stronger evidence (smaller p-value) to reject H0H_0.

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 4 hard

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

← All P-Value Examples P-Value Concept