**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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Description: **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 consid

If p-value > significance level, then the we fail to reject null Hypothesis If p-value <…

Math

Statistics

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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