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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**Hypothesis Testing Guide: Proportion of Elementary School Districts Named Anderson** **Hypothesis Statement:** Test the hypothesis that the proportion of Elementary School Districts being Anderson has increased from 30%. **Instructions:** a) **Hypotheses Expression:** - Express the null and alternative hypotheses in symbolic form for this claim. - Enter your answer as a decimal. For example, if you have 35%, enter 0.35. - Remember to enter a zero in front of the decimal point. However, if you have a percentage that is a multiple of 10, do not include the 0 after the number. For example, if you have 20%, enter 0.2, not 0.20. - \( H_0: \) [Enter Text Box] - \( H_a: \) [Enter Text Box] **Parameters:** - Proportion: enter \( p \) - Mean: enter \( \mu \) **Symbol Codes:** - \( \ge \): enter >= - \( \le \): enter <= - \( \neq \): enter != b) **Test Statistic Calculation:** - Find the test statistic. Round to two decimal places. - [Enter Text Box] c) **P-Value Calculation:** - What is the p-value? Round to four decimals. - \( p = \) [Enter Text Box] d) **Decision Making:** - Make a decision based on a 0.01 significance level. - [ ] Do not reject the null - [ ] Reject the null e) **Conclusion:** - What is the conclusion? - [Enter Text Box]
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Transcribed Image Text:**Hypothesis Testing Guide: Proportion of Elementary School Districts Named Anderson** **Hypothesis Statement:** Test the hypothesis that the proportion of Elementary School Districts being Anderson has increased from 30%. **Instructions:** a) **Hypotheses Expression:** - Express the null and alternative hypotheses in symbolic form for this claim. - Enter your answer as a decimal. For example, if you have 35%, enter 0.35. - Remember to enter a zero in front of the decimal point. However, if you have a percentage that is a multiple of 10, do not include the 0 after the number. For example, if you have 20%, enter 0.2, not 0.20. - \( H_0: \) [Enter Text Box] - \( H_a: \) [Enter Text Box] **Parameters:** - Proportion: enter \( p \) - Mean: enter \( \mu \) **Symbol Codes:** - \( \ge \): enter >= - \( \le \): enter <= - \( \neq \): enter != b) **Test Statistic Calculation:** - Find the test statistic. Round to two decimal places. - [Enter Text Box] c) **P-Value Calculation:** - What is the p-value? Round to four decimals. - \( p = \) [Enter Text Box] d) **Decision Making:** - Make a decision based on a 0.01 significance level. - [ ] Do not reject the null - [ ] Reject the null e) **Conclusion:** - What is the conclusion? - [Enter Text Box]
**Data Summary** Counts and Percentages: Elementary School | | Anderson | Others | Total | |----------------|----------|--------|-------| | Count | 241 | 560 | 801 | | Percentage | 30.08739 | 69.91261 | 100 | --- **Test of Hypothesis: Elementary School** *Method: Large Sample z Test (Using p0)* *Alternative Hypothesis \(H_a\): Proportion of 'Anderson' is greater than 0.3* | Sample Proportion | Std Error | Standardized Obs Stat | 1% z-Upper Critical | P-Value | BFB | |-------------------|-----------|-----------------------|---------------------|----------|------| | 0.300874 | 0.0161917 | 0.0539725 | 2.32635 | 0.478479 | 1 | - Test is not significant at 1% level. - Bayes Factor Bound (BFB): The data imply the odds in favor of the alternative hypothesis is at most 1 to 1, relative to the null hypothesis. --- **P-value Graph: Large Sample z (Using p0)** - *Null density (in units of data): Normal; mean = 0.3, sd = 0.0161917.* - *Alternative Hypothesis \(H_a\): Proportion of 'Anderson' is greater than 0.3.* Graph Explanation: - **Observed Data Scale**: The graph shows the distribution of the observed data with an emphasized area (in red) representing the observed sample proportion (0.30087) and the p-value (0.47848). - **Standard Normal (z) Scale**: The graph presents the distribution on a standard normal scale, with the observed z statistic (0.053972) and the corresponding p-value (0.47848) highlighted. The graphs visually compare the observed data and the standard normal distribution, illustrating the hypothesis testing results.
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Transcribed Image Text:**Data Summary** Counts and Percentages: Elementary School | | Anderson | Others | Total | |----------------|----------|--------|-------| | Count | 241 | 560 | 801 | | Percentage | 30.08739 | 69.91261 | 100 | --- **Test of Hypothesis: Elementary School** *Method: Large Sample z Test (Using p0)* *Alternative Hypothesis \(H_a\): Proportion of 'Anderson' is greater than 0.3* | Sample Proportion | Std Error | Standardized Obs Stat | 1% z-Upper Critical | P-Value | BFB | |-------------------|-----------|-----------------------|---------------------|----------|------| | 0.300874 | 0.0161917 | 0.0539725 | 2.32635 | 0.478479 | 1 | - Test is not significant at 1% level. - Bayes Factor Bound (BFB): The data imply the odds in favor of the alternative hypothesis is at most 1 to 1, relative to the null hypothesis. --- **P-value Graph: Large Sample z (Using p0)** - *Null density (in units of data): Normal; mean = 0.3, sd = 0.0161917.* - *Alternative Hypothesis \(H_a\): Proportion of 'Anderson' is greater than 0.3.* Graph Explanation: - **Observed Data Scale**: The graph shows the distribution of the observed data with an emphasized area (in red) representing the observed sample proportion (0.30087) and the p-value (0.47848). - **Standard Normal (z) Scale**: The graph presents the distribution on a standard normal scale, with the observed z statistic (0.053972) and the corresponding p-value (0.47848) highlighted. The graphs visually compare the observed data and the standard normal distribution, illustrating the hypothesis testing results.
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