Suppose the p-value for a two-tailed test equals 0.0463 and the level of significance equals 2.5%. What is the decision of the test? Suppose the p-value for a two-tailed test equals 0.0241 and the level of significance equals 2.5%. What is the decision of the test?
Suppose the p-value for a two-tailed test equals 0.0463 and the level of significance equals 2.5%. What is the decision of the test? Suppose the p-value for a two-tailed test equals 0.0241 and the level of significance equals 2.5%. What is the decision of the test?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Hypothesis Testing Decisions**
When conducting hypothesis tests, the decision whether to reject or fail to reject the null hypothesis is guided by comparing the p-value of the test to the predetermined level of significance (alpha, α). Let’s consider two scenarios to understand this better:
1. **Scenario 1: P-Value is 0.0463 and α = 2.5%**
Suppose the p-value for a two-tailed test equals 0.0463 and the level of significance equals 2.5%.
**Question:** What is the decision of the test?
**Explanation:**
- The level of significance (α) is 2.5%, which is equivalent to 0.025.
- Compare the p-value (0.0463) with α (0.025).
- Since 0.0463 > 0.025, we fail to reject the null hypothesis.
**Conclusion:** The p-value of 0.0463 is greater than the level of significance at 2.5%, hence we do not have sufficient evidence to reject the null hypothesis.
2. **Scenario 2: P-Value is 0.0241 and α = 2.5%**
Suppose the p-value for a two-tailed test equals 0.0241 and the level of significance equals 2.5%.
**Question:** What is the decision of the test?
**Explanation:**
- The level of significance (α) is 2.5%, which is equivalent to 0.025.
- Compare the p-value (0.0241) with α (0.025).
- Since 0.0241 < 0.025, we reject the null hypothesis.
**Conclusion:** The p-value of 0.0241 is less than the level of significance at 2.5%, hence we have sufficient evidence to reject the null hypothesis.
The decision in hypothesis testing hinges on this critical comparison between the p-value and the significance level. Observing whether the p-value is smaller or larger than α directly informs us of the statistical significance of our test results.
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