MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Analyzing Voting Patterns Among College Students #### Data Collection A pollster gathered voting preferences from a sample of 350 college students. The distribution of votes across different political affiliations and academic years is provided in the table below: | Political Affiliation | Freshmen | Sophomore | Junior | Senior | Total | |-----------------------|----------|-----------|--------|--------|-------| | Democratic | 20 | 15 | 12 | 15 | 62 | | Green | 30 | 28 | 20 | 30 | 108 | | Independent | 25 | 30 | 20 | 20 | 95 | | Republican | 30 | 20 | 15 | 20 | 85 | | **Total** | 105 | 93 | 67 | 85 | 350 | #### Hypothesis Testing To determine if overall voting patterns are consistent across different academic years, a hypothesis test is conducted using MINITAB software, with a significance level (\(\alpha\)) of 0.05. ##### Steps to Test the Hypothesis: 1. **Identify the Parameters**: - **Parameters**: The number of votes in each political affiliation category for different academic years. 2. **Null Hypothesis (H₀)**: - The voting patterns are similar across the academic years. i.e., the distribution of voting preferences does not depend on the academic year. 3. **Alternative Hypothesis (H₁)**: - The voting patterns are different across the academic years. i.e., the distribution of voting preferences depends on the academic year. 4. **Test Statistics**: - Utilize a chi-square test for independence to compare the observed frequencies in the table with the expected frequencies if the null hypothesis were true. 5. **p-value**: - The p-value from the chi-square test will be used to determine the statistical significance of the results. 6. **Conclusion**: - Based on the p-value, if \( p \leq 0.05 \), reject the null hypothesis. Otherwise, do not reject the null hypothesis. By performing these steps, we can understand whether there are significant differences in political voting patterns among college students based on their academic year.
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Transcribed Image Text:### Analyzing Voting Patterns Among College Students #### Data Collection A pollster gathered voting preferences from a sample of 350 college students. The distribution of votes across different political affiliations and academic years is provided in the table below: | Political Affiliation | Freshmen | Sophomore | Junior | Senior | Total | |-----------------------|----------|-----------|--------|--------|-------| | Democratic | 20 | 15 | 12 | 15 | 62 | | Green | 30 | 28 | 20 | 30 | 108 | | Independent | 25 | 30 | 20 | 20 | 95 | | Republican | 30 | 20 | 15 | 20 | 85 | | **Total** | 105 | 93 | 67 | 85 | 350 | #### Hypothesis Testing To determine if overall voting patterns are consistent across different academic years, a hypothesis test is conducted using MINITAB software, with a significance level (\(\alpha\)) of 0.05. ##### Steps to Test the Hypothesis: 1. **Identify the Parameters**: - **Parameters**: The number of votes in each political affiliation category for different academic years. 2. **Null Hypothesis (H₀)**: - The voting patterns are similar across the academic years. i.e., the distribution of voting preferences does not depend on the academic year. 3. **Alternative Hypothesis (H₁)**: - The voting patterns are different across the academic years. i.e., the distribution of voting preferences depends on the academic year. 4. **Test Statistics**: - Utilize a chi-square test for independence to compare the observed frequencies in the table with the expected frequencies if the null hypothesis were true. 5. **p-value**: - The p-value from the chi-square test will be used to determine the statistical significance of the results. 6. **Conclusion**: - Based on the p-value, if \( p \leq 0.05 \), reject the null hypothesis. Otherwise, do not reject the null hypothesis. By performing these steps, we can understand whether there are significant differences in political voting patterns among college students based on their academic year.
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