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### Analysis of Baseball Fans' Opinions on the New Commissioner's Performance In a study involving 100 baseball fans from four regions of the country, opinions were collected on the new commissioner's job performance. The table below summarizes the observed and expected values, along with the Chi-squared (\( \chi^2 \)) contributions from each region. #### Hypotheses - **\( H_0 \):** The variables are independent. - **\( H_a \):** At least two variables are dependent (claim). #### Observed Values | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 41 | 29 | 34 | | Southeast | 44 | 28 | 32 | | Midwest | 57 | 26 | 21 | | West | 49 | 25 | 30 | #### Expected Values | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 47.75 | 27 | 29.25 | | Southeast | 47.75 | 27 | 29.25 | | Midwest | 47.75 | 27 | 29.25 | | West | 47.75 | 27 | 29.25 | #### \( R^2 \) Contributions | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 0.954 | 0.148 | 0.771 | | Southeast | 0.295 | 0.037 | 0.259 | | Midwest | 1.792 | 0.037 | 2.327 | | West | 0.033 | 0.148 | 0.019 | ### Statistical Decision The question posed is whether there is enough evidence to reject \( H_0 \) and support the claim of dependency at the 0.10 level of significance. #### Options for Decision A. Yes, the test statistic \( \chi^2 = 10.645 \) is in the rejection region with critical value 6.82. B.

### Analysis of Baseball Fans' Opinions on the New Commissioner's Performance In a study involving 100 baseball fans from four regions of the country, opinions were collected on the new commissioner's job performance. The table below summarizes the observed and expected values, along with the Chi-squared (\( \chi^2 \)) contributions from each region. #### Hypotheses - **\( H_0 \):** The variables are independent. - **\( H_a \):** At least two variables are dependent (claim). #### Observed Values | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 41 | 29 | 34 | | Southeast | 44 | 28 | 32 | | Midwest | 57 | 26 | 21 | | West | 49 | 25 | 30 | #### Expected Values | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 47.75 | 27 | 29.25 | | Southeast | 47.75 | 27 | 29.25 | | Midwest | 47.75 | 27 | 29.25 | | West | 47.75 | 27 | 29.25 | #### \( R^2 \) Contributions | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 0.954 | 0.148 | 0.771 | | Southeast | 0.295 | 0.037 | 0.259 | | Midwest | 1.792 | 0.037 | 2.327 | | West | 0.033 | 0.148 | 0.019 | ### Statistical Decision The question posed is whether there is enough evidence to reject \( H_0 \) and support the claim of dependency at the 0.10 level of significance. #### Options for Decision A. Yes, the test statistic \( \chi^2 = 10.645 \) is in the rejection region with critical value 6.82. B.

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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### Analysis of Baseball Fans' Opinions on the New Commissioner's Performance In a study involving 100 baseball fans from four regions of the country, opinions were collected on the new commissioner's job performance. The table below summarizes the observed and expected values, along with the Chi-squared (\( \chi^2 \)) contributions from each region. #### Hypotheses - **\( H_0 \):** The variables are independent. - **\( H_a \):** At least two variables are dependent (claim). #### Observed Values | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 41 | 29 | 34 | | Southeast | 44 | 28 | 32 | | Midwest | 57 | 26 | 21 | | West | 49 | 25 | 30 | #### Expected Values | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 47.75 | 27 | 29.25 | | Southeast | 47.75 | 27 | 29.25 | | Midwest | 47.75 | 27 | 29.25 | | West | 47.75 | 27 | 29.25 | #### \( R^2 \) Contributions | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 0.954 | 0.148 | 0.771 | | Southeast | 0.295 | 0.037 | 0.259 | | Midwest | 1.792 | 0.037 | 2.327 | | West | 0.033 | 0.148 | 0.019 | ### Statistical Decision The question posed is whether there is enough evidence to reject \( H_0 \) and support the claim of dependency at the 0.10 level of significance. #### Options for Decision A. Yes, the test statistic \( \chi^2 = 10.645 \) is in the rejection region with critical value 6.82. B.
Transcribed Image Text:### Analysis of Baseball Fans' Opinions on the New Commissioner's Performance In a study involving 100 baseball fans from four regions of the country, opinions were collected on the new commissioner's job performance. The table below summarizes the observed and expected values, along with the Chi-squared (\( \chi^2 \)) contributions from each region. #### Hypotheses - **\( H_0 \):** The variables are independent. - **\( H_a \):** At least two variables are dependent (claim). #### Observed Values | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 41 | 29 | 34 | | Southeast | 44 | 28 | 32 | | Midwest | 57 | 26 | 21 | | West | 49 | 25 | 30 | #### Expected Values | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 47.75 | 27 | 29.25 | | Southeast | 47.75 | 27 | 29.25 | | Midwest | 47.75 | 27 | 29.25 | | West | 47.75 | 27 | 29.25 | #### \( R^2 \) Contributions | Region | Favorable | Unfavorable | No Opinion | |------------|-----------|-------------|------------| | Northeast | 0.954 | 0.148 | 0.771 | | Southeast | 0.295 | 0.037 | 0.259 | | Midwest | 1.792 | 0.037 | 2.327 | | West | 0.033 | 0.148 | 0.019 | ### Statistical Decision The question posed is whether there is enough evidence to reject \( H_0 \) and support the claim of dependency at the 0.10 level of significance. #### Options for Decision A. Yes, the test statistic \( \chi^2 = 10.645 \) is in the rejection region with critical value 6.82. B.
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