Interpreting a P-Value In Exercises 3–8, the P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a)α=0.01, (b) α=0.05 , and (c) α=0.10.


P = 0.0838

Verified step by step guidance

1. Step 1: Recall the decision rule for hypothesis testing. If the P-value is less than or equal to the level of significance (α), reject the null hypothesis (H₀). Otherwise, fail to reject H₀.
2. Step 2: Compare the given P-value (P = 0.0838) to the first level of significance, α = 0.01. Determine whether P ≤ α or P > α.
3. Step 3: Compare the given P-value (P = 0.0838) to the second level of significance, α = 0.05. Determine whether P ≤ α or P > α.
4. Step 4: Compare the given P-value (P = 0.0838) to the third level of significance, α = 0.10. Determine whether P ≤ α or P > α.
5. Step 5: Based on the comparisons in Steps 2, 3, and 4, state whether to reject or fail to reject H₀ for each level of significance (α = 0.01, 0.05, and 0.10).

Key Concepts

P-Value

The P-value is a statistical measure that helps determine the significance of results in hypothesis testing. It represents the probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis (H0) is true. A lower P-value indicates stronger evidence against H0, while a higher P-value suggests weaker evidence.

Null Hypothesis (H0)

The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing. Researchers aim to gather evidence to either reject or fail to reject H0 based on the data collected. Understanding H0 is crucial for interpreting the results of a hypothesis test and the associated P-value.

Level of Significance (α)

The level of significance (α) is a threshold set by the researcher before conducting a hypothesis test, which determines the criteria for rejecting the null hypothesis. Common values for α are 0.01, 0.05, and 0.10. If the P-value is less than or equal to α, H0 is rejected; if it is greater, H0 is not rejected. This concept is essential for making informed decisions based on statistical evidence.