### ANOVA Analysis ContextWhen conducting a one-way ANOVA, the following table is used to summarize the sources of variation, degrees of freedom, and the sum of squares:| Sources of Variation | Degrees of Freedom | Sum of Squares ||----------------------|--------------------|----------------|| Between | 4 | 200 || Within | 45 | 3547 |### Explanation and ProblemThe calculated p-value for testing the equality of the means of all populations is 0.6406. This indicates that at the current sample sizes, the means are not significantly different at the common significance level of 5%.#### Task:Suppose you wish to increase the sample sizes for all groups equally. The miraculous condition you're working with is that the sum of squares both within and between samples remains unchanged when adjusting the sample sizes.The problem asks: What are the smallest possible sample sizes for groups that would lead to a significant result at the 5% significance level?There is a text box labeled "Sample sizes = " for input.### Key Considerations- Increasing sample size can affect the F-ratio, potentially making the groups significantly different.- You need to calculate the smallest sample size that allows the p-value to fall below 0.05, assuming the observed variances remain constant.This information aids in understanding the mechanics of ANOVA and the influence of sample size on statistical significance.

The degrees of freedom between the source of variation is K-1=4 i.e. K=5 The degrees of freedom…

Suppose you are performing a one-way ANOVA with only the information given in the following table. Sources of Variation Degrees of Freedom Sum of Squares Between 4 200 Within 45 3547 The p-value for the test of the equality of the means of all populations is calculated to be 0.6406. Suppose you plan to increase the sample sizes for all groups but keep them all equal. However, when you do this, the sum of squares within samples and the sum of squares between samples (magically) remain the same. What are the smallest sample sizes for groups that would make this result significant at the 5% significance level? Sample sizes = i

Suppose you are performing a one-way ANOVA with only the information given in the following table. Sources of Variation Degrees of Freedom Sum of Squares Between 4 200 Within 45 3547 The p-value for the test of the equality of the means of all populations is calculated to be 0.6406. Suppose you plan to increase the sample sizes for all groups but keep them all equal. However, when you do this, the sum of squares within samples and the sum of squares between samples (magically) remain the same. What are the smallest sample sizes for groups that would make this result significant at the 5% significance level? Sample sizes = i

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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