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 = 0.0062

Verified step by step guidance

1. Step 1: Understand the problem. The P-value is a measure of the strength of evidence against the null hypothesis (H0). A smaller P-value indicates stronger evidence to reject H0. The decision to reject H0 depends on comparing the P-value to the significance level (α).
2. Step 2: Recall the decision rule. If the P-value is less than the significance level (α), reject the null hypothesis (H0). Otherwise, fail to reject H0.
3. Step 3: Compare the P-value (P = 0.0062) to the significance level α = 0.01. If P < α, reject H0; otherwise, fail to reject H0.
4. Step 4: Compare the P-value (P = 0.0062) to the significance level α = 0.05. If P < α, reject H0; otherwise, fail to reject H0.
5. Step 5: Compare the P-value (P = 0.0062) to the significance level α = 0.10. If P < α, reject H0; otherwise, fail to reject H0.

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 smaller P-value indicates stronger evidence against H0, suggesting that the null hypothesis may be rejected.

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, the null hypothesis is rejected, indicating that the results are statistically significant.