### Understanding the Impact on Test PowerThe power of a statistical test is influenced by various factors. Let's examine how the power of the test changes under the following scenarios:1. **What is the effect on the power of the test for the following scenarios:** a. β (beta) is increased b. β (beta) is decreased c. α (alpha) is increased d. α (alpha) is decreased e. n (sample size) is increased f. n (sample size) is decreased ---#### Explanation:- **a. β (beta) is increased:** Beta (β) represents the probability of making a Type II error, which is failing to reject a false null hypothesis. If β is increased, it means that the likelihood of making a Type II error is higher, and thus the power of the test (which is 1 - β) decreases.- **b. β (beta) is decreased:** Conversely, if β is decreased, the probability of making a Type II error is lower, which means the power of the test increases.- **c. α (alpha) is increased:** Alpha (α) is the probability of making a Type I error, which is rejecting a true null hypothesis. By increasing α, you also increase the test's power, since the critical region for rejecting the null hypothesis becomes larger.- **d. α (alpha) is decreased:** Decreasing α results in a smaller critical region, which in turn decreases the power of the test, as there's a lower probability of rejecting the null hypothesis when it is false.- **e. n (sample size) is increased:** Increasing the sample size (n) generally increases the power of the test. A larger sample size provides more information about the population, reducing the standard error and making it easier to detect a true effect.- **f. n (sample size) is decreased:** Decreasing the sample size reduces the power of the test. With a smaller sample size, there is higher variability in the data, making it more difficult to detect a true effect.Understanding how these factors influence the power of a test is crucial for designing experiments and making accurate inferences from data.

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Description: ### Understanding the Impact on Test PowerThe power of a statistical test is influenced by various factors. Let's examine how the power of the test changes under the following scenarios:1. **What is the effect on the power of the test for the follow

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Math

Statistics

11. What is the effect on the power of the test for the following scenarios: a. Bis increased b. Bis decreased c. a is increased d. a is decreased e. n is increased f. n is decreased

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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