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You are running an Analysis of Variance to test if there is a difference in the average lengths of college football games in three conferences: The Big 12, Big 10 and SEC Ho:1 = = 3: The average lengths of games are the same. Ha: At least one conference has average lengths of games different from the others.(claim) a = 0.10 Times in minutes (Group 1) Big 12 (Group 2) Big 10 (Group 3) SEC 222 211 218 240 201 214 254 202 214 224 201 218 259 187 227 229 Round all values including all intermediate calculations to 2 decimal places Fill in the summary table for the means, grand mean and sum of squares Big 12 Big 10. SEC Grand Mean i S, The Sum of Squares within each group SS = One Way Analysis of Variance (ANOVA)

You are running an Analysis of Variance to test if there is a difference in the average lengths of college football games in three conferences: The Big 12, Big 10 and SEC Ho:1 = = 3: The average lengths of games are the same. Ha: At least one conference has average lengths of games different from the others.(claim) a = 0.10 Times in minutes (Group 1) Big 12 (Group 2) Big 10 (Group 3) SEC 222 211 218 240 201 214 254 202 214 224 201 218 259 187 227 229 Round all values including all intermediate calculations to 2 decimal places Fill in the summary table for the means, grand mean and sum of squares Big 12 Big 10. SEC Grand Mean i S, The Sum of Squares within each group SS = One Way Analysis of Variance (ANOVA)

MATLAB: An Introduction with Applications
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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**ANOVA Test Summary** ### Between Groups (Numerator) - **Sum of Squares Between (SSₐ):** \( SS_B = \sum n_i (\bar{x}_i - \bar{x})^2 \) - **Degrees of Freedom Between (dfₐ):** \( df_B = df_k = k - 1 \) - **Mean Squares Between (MSₐ):** \( MS_B = \frac{SS_B}{df_B} \) ### Within Groups (Denominator) - **Sum of Squares Within (SSᵥᵂ):** \( SS_{vw} = SS_W = \sum \sum (x - x_j)^2 \) - **Degrees of Freedom Within (dfᵥᵂ):** \( df_{vw} = df_D = N - k \) - **Mean Squares Within (MSᵥᵂ):** \( MS_{vw} = \frac{SS_{vw}}{df_{vw}} \) ### Total - **Total Sum of Squares (SSᴛ):** \( SS_T = SS_B + SS_{vw} \) - **Total Degrees of Freedom (dfᴛ):** \( df_T = df_B + df_{vw} \) ### Definitions: - **\( \bar{x}_i \):** Mean of each group - **\( \bar{x} \):** Grand Mean: Mean of all data points - **\( SS_B \):** Sum of Squares between groups - **\( SS_{vw} \):** Sum of Squares within each group - **\( df_B \):** Degrees of Freedom between groups - **\( df_{vw} \):** Degrees of Freedom within each group - **\( N \):** Total number of data points in all groups - **\( k \):** Number of groups - **\( MS_B \):** Mean of the Squares between groups - **\( MS_{vw} \):** Mean of the Squares within each group ### Fill in the Summary Table for the ANOVA Test: | | SS | df | MS | F | |-----------|-----|----|-----|---| | Between | | | | | | Within | | | | | | Total
Transcribed Image Text:**ANOVA Test Summary** ### Between Groups (Numerator) - **Sum of Squares Between (SSₐ):** \( SS_B = \sum n_i (\bar{x}_i - \bar{x})^2 \) - **Degrees of Freedom Between (dfₐ):** \( df_B = df_k = k - 1 \) - **Mean Squares Between (MSₐ):** \( MS_B = \frac{SS_B}{df_B} \) ### Within Groups (Denominator) - **Sum of Squares Within (SSᵥᵂ):** \( SS_{vw} = SS_W = \sum \sum (x - x_j)^2 \) - **Degrees of Freedom Within (dfᵥᵂ):** \( df_{vw} = df_D = N - k \) - **Mean Squares Within (MSᵥᵂ):** \( MS_{vw} = \frac{SS_{vw}}{df_{vw}} \) ### Total - **Total Sum of Squares (SSᴛ):** \( SS_T = SS_B + SS_{vw} \) - **Total Degrees of Freedom (dfᴛ):** \( df_T = df_B + df_{vw} \) ### Definitions: - **\( \bar{x}_i \):** Mean of each group - **\( \bar{x} \):** Grand Mean: Mean of all data points - **\( SS_B \):** Sum of Squares between groups - **\( SS_{vw} \):** Sum of Squares within each group - **\( df_B \):** Degrees of Freedom between groups - **\( df_{vw} \):** Degrees of Freedom within each group - **\( N \):** Total number of data points in all groups - **\( k \):** Number of groups - **\( MS_B \):** Mean of the Squares between groups - **\( MS_{vw} \):** Mean of the Squares within each group ### Fill in the Summary Table for the ANOVA Test: | | SS | df | MS | F | |-----------|-----|----|-----|---| | Between | | | | | | Within | | | | | | Total
**Analysis of Variance on College Football Game Lengths** This document outlines an Analysis of Variance (ANOVA) to test whether there is a difference in the average lengths of college football games among three conferences: the Big 12, Big 10, and SEC. ### Hypotheses - **Null Hypothesis (\(H_0\))**: \(\mu_1 = \mu_2 = \mu_3\) — The average lengths of games are the same across all conferences. - **Alternative Hypothesis (\(H_a\))**: At least one conference has an average game length different from the others (claim). ### Significance Level - \(\alpha = 0.10\) ### Data Table: Times in Minutes \[ \begin{array}{|c|c|c|} \hline \text{(Group 1) Big 12} & \text{(Group 2) Big 10} & \text{(Group 3) SEC} \\ \hline 222 & 211 & 218 \\ 240 & 201 & 214 \\ 254 & 202 & 214 \\ 224 & 201 & 218 \\ 259 & 187 & 227 \\ 229 & & \\ \hline \end{array} \] ### Instructions - Round all values, including all intermediate calculations, to 2 decimal places. - Fill in the summary table for the means, grand mean, and sum of squares. ### Summary Table \[ \begin{array}{|c|c|c|c|} \hline & \text{Big 12} & \text{Big 10} & \text{SEC} & \text{Grand} \\ \hline \text{Mean } \bar{x} & & & & \\ \hline SS_i & & & & \\ \hline \end{array} \] ### Equation - **Sum of Squares within each group**: \[ SS_i = \sum (x - \bar{x})^2 \] ### Methodology This is a One-Way Analysis of Variance (ANOVA).
Transcribed Image Text:**Analysis of Variance on College Football Game Lengths** This document outlines an Analysis of Variance (ANOVA) to test whether there is a difference in the average lengths of college football games among three conferences: the Big 12, Big 10, and SEC. ### Hypotheses - **Null Hypothesis (\(H_0\))**: \(\mu_1 = \mu_2 = \mu_3\) — The average lengths of games are the same across all conferences. - **Alternative Hypothesis (\(H_a\))**: At least one conference has an average game length different from the others (claim). ### Significance Level - \(\alpha = 0.10\) ### Data Table: Times in Minutes \[ \begin{array}{|c|c|c|} \hline \text{(Group 1) Big 12} & \text{(Group 2) Big 10} & \text{(Group 3) SEC} \\ \hline 222 & 211 & 218 \\ 240 & 201 & 214 \\ 254 & 202 & 214 \\ 224 & 201 & 218 \\ 259 & 187 & 227 \\ 229 & & \\ \hline \end{array} \] ### Instructions - Round all values, including all intermediate calculations, to 2 decimal places. - Fill in the summary table for the means, grand mean, and sum of squares. ### Summary Table \[ \begin{array}{|c|c|c|c|} \hline & \text{Big 12} & \text{Big 10} & \text{SEC} & \text{Grand} \\ \hline \text{Mean } \bar{x} & & & & \\ \hline SS_i & & & & \\ \hline \end{array} \] ### Equation - **Sum of Squares within each group**: \[ SS_i = \sum (x - \bar{x})^2 \] ### Methodology This is a One-Way Analysis of Variance (ANOVA).
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