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MATLAB: An Introduction with Applications

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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**Understanding Hypothesis Testing: Making Conclusions**

When conducting a hypothesis test, particularly using a z-score, it's crucial to determine if the test statistic falls within the critical region. The critical region is defined by the significance level (alpha) of the test and represents the area where the null hypothesis \( H_0 \) is unlikely to be true.

**Question:**
If the sample data produce a test statistic (z-score) that is in the critical region, then which of the following is the appropriate conclusion for the test?

- ⬤ reject \( H_1 \)
- ⬤ fail to reject \( H_1 \)
- ⬤ fail to reject \( H_0 \)
- ⬤ reject \( H_0 \)

**Key Concept:**

- **Reject \( H_0 \):** If the test statistic falls into the critical region, it means there is sufficient evidence to conclude that the null hypothesis is not true. Thus, the correct action is to reject \( H_0 \).

**Conclusion:**

When the test statistic is in the critical region, the conclusion is to reject the null hypothesis \( H_0 \). This suggests that the sample data provide enough evidence against \( H_0 \), favoring the alternative hypothesis \( H_1 \).

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