P-Value Statistics Example 1

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

Example 1

hard
A two-tailed z-test gives z=โˆ’2.65z = -2.65. The p-value is approximately 0.008. If ฮฑ=0.05\alpha = 0.05, should we reject H0H_0?

Solution

  1. 1
    Step 1: Compare the p-value to the significance level: 0.008<0.050.008 < 0.05.
  2. 2
    Step 2: Since p<ฮฑp < \alpha, we reject H0H_0.
  3. 3
    Step 3: There is statistically significant evidence that the population mean differs from the claimed value.

Answer

Reject H0H_0. The result is statistically significant at the 0.05 level.
The p-value is the probability of obtaining results at least as extreme as observed, assuming H0H_0 is true. A small p-value (below ฮฑ\alpha) provides evidence against 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 โ†’

More P-Value Examples

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]?

Example 4 hard

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

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