**Question:**You would first reject the same test statistic \( \chi^2_0 \) at a higher significance level if the degrees of freedom were higher.- ☐ True- ☐ False**Explanation:**This question is addressing the relationship between the chi-square test statistic, significance levels, and degrees of freedom in statistical hypothesis testing.**Concept Overview:**In a chi-square test, the test statistic \( \chi^2 \) is compared to a critical value from the chi-square distribution to decide whether to reject the null hypothesis. The critical value depends on two factors:1. **Degrees of Freedom (df):** Increases in degrees of freedom typically cause the chi-square distribution to spread out, therefore requiring higher test statistic values to reach the same level of significance. 2. **Significance Level (α):** Represents the probability of rejecting the null hypothesis when it is true (Type I error). A higher significance level (e.g., 0.10 vs. 0.05) means a less stringent criterion for rejection.**Answer:**The statement given is false. If the degrees of freedom were higher, for the same significance level, the critical value increases. Therefore, you would not reject the test statistic at the same or a higher significance level due to the increase in the threshold needed for rejection.

given data we have to find the statement is true or false. we would first reject the same test…

Answered: You would first reject the same 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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You would first reject the same test statistic x at a higher significance level if the degrees of freedom were higher. True False