**Exercise 22 Explanation for Educational Website:**This exercise involves modifying data from a previous problem (Problem 21) by doubling the sample size to \( n = 10 \) while keeping the same sample means and variances. The task is to analyze how this change impacts the F-ratio using ANOVA. The data is presented in a table divided into three treatments (I, II, and III).**Table Layout:**- Each treatment has the following parameters: - **n**: Sample size \( (n = 10) \) - **M**: Sample mean - **T**: Total sum of scores in the treatment - **s²**: Sample variance - **SS**: Sum of squares for the treatment**Treatment Details:**- **Treatment I:** - \( n = 10 \) - \( M = 1 \) - \( T = 10 \) - \( s² = 9.00 \) - \( SS = 81 \)- **Treatment II:** - \( n = 10 \) - \( M = 5 \) - \( T = 50 \) - \( s² = 10.00 \) - \( SS = 90 \)- **Treatment III:** - \( n = 10 \) - \( M = 6 \) - \( T = 60 \) - \( s² = 11.00 \) - \( SS = 99 \)**Overall Data:**- Total sum of all treatments (\( \Sigma X² = 890 \))- \( N = 30 \) (Total number of data points across all treatments)- Grand total (\( G = 120 \))**Exercise Requirement:**a. **Prediction and Analysis:** - Predict how increasing the sample size affects the F-ratio for these data compared to the values from Problem 21. - Use an ANOVA with \( \alpha = 0.05 \) to test this prediction. - Note: Since the samples are of the same size, \( MS_{within} \) (Mean Square Within) is the average of the three sample variances.This exercise provides a hands-on understanding of how sample size influences statistical analysis using the ANOVA method.

I II III n=10 n=10 n=10 M=1 M=5 M=6 N=30 T=10 T=50 T=60 G=120 s2=9.00 s2=10.00 s2=11.00 ∑Xi2=890 SS=81 SS=90 SS=99 level of significance α=0.05 The increase in the sample size increases the value of the F-ratio. Since a large sample size the smaller differences in means. Now to state the null hypothesis and alternate hypothesis is given below, H0:μ1=μ2=μ3All treatments have equal effectsH1:Atleast one of the treatment mean is different Now, dfbetw=k-1=3-1dfbetw=2now to find dfwithin,dfwithin=9+9+9dfwithin=27 Here, G=10+50+60 G=120 Now to find SSbetw,SSbetw=∑nixi2-G2N=10×12+52+62-120230=10×1+25+36-1440030=10×62-480=620-480=140SSbetw=140 To calculate MSbetw,MSbetw=SSbetwdfbetw=1402=70to calculate MSwithin,MSwithin=9.00+10.00+11.003=303=10 To calculate F statistic as below,F=MSbetwMSwithin=7010=7Fcritic=Fdf1,df2,α2=F0.025,2,27=4.242F>Fcritic i.e. 7>4.242 i.e. H0 is rejected at a 0.05 level of significance. We reject H0 means we accept Ha i.e. atleast one of the treatmenrt means is different.

Answered: 22. To create the following data we…

Math

Statistics

22. To create the following data we started with the same sample means and variances that appeared in problem 21 but doubled the sample size to n 10. Treatment

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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