A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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**Title: Analysis of Racial Distribution in Work-Study Programs**

**Introduction:**
This document explores whether the racial distribution for students on work-study differs from those not on work-study, utilizing statistical analysis at a 0.05 significance level.

**Data Overview:**

- **Contingency Table:**

  |                        | White | Black | Hispanic | Asian | Other |
  |------------------------|-------|-------|----------|-------|-------|
  | Work Study             | 96    | 44    | 78       | 53    | 28    |
  | Not Work Study         | 82    | 66    | 108      | 86    | 32    |

- **R Vector Data:** 96, 82, 44, 66, 78, 108, 53, 86, 28, 32

**Analysis Steps:**

1. **Statistical Test Selection:**
   - **a.** Choose the correct test for analyzing the data.

2. **Hypotheses Formation:**
   - **b.** Define the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_1\)).

3. **Calculation of Test Statistic:**
   - **c.** Compute the test-statistic and report the value to three decimal places.

4. **Determination of P-Value:**
   - **d.** Calculate and present the p-value to four decimal places.

5. **Comparison of P-Value and Significance Level:**
   - **e.** Assess if the p-value is less than or equal to \(\alpha\).

6. **Decision Making:**
   - **f.** Based on the comparison, make a decision to reject or fail to reject the null hypothesis.

7. **Conclusion:**
   - **g.** Draw an overall conclusion:
      - Option 1: At the 5% significance level, there is insufficient evidence to conclude a difference in racial distribution.
      - Option 2: At the 5% significance level, there is sufficient evidence to conclude a difference in racial distribution.

**Conclusion:**
This guide will help assess whether there is a significant difference in the racial distribution between students involved in work-study programs and those who are not. Decisions are made based on the computed statistical analyses and relevant hypothesis testing results.
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Transcribed Image Text:**Title: Analysis of Racial Distribution in Work-Study Programs** **Introduction:** This document explores whether the racial distribution for students on work-study differs from those not on work-study, utilizing statistical analysis at a 0.05 significance level. **Data Overview:** - **Contingency Table:** | | White | Black | Hispanic | Asian | Other | |------------------------|-------|-------|----------|-------|-------| | Work Study | 96 | 44 | 78 | 53 | 28 | | Not Work Study | 82 | 66 | 108 | 86 | 32 | - **R Vector Data:** 96, 82, 44, 66, 78, 108, 53, 86, 28, 32 **Analysis Steps:** 1. **Statistical Test Selection:** - **a.** Choose the correct test for analyzing the data. 2. **Hypotheses Formation:** - **b.** Define the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_1\)). 3. **Calculation of Test Statistic:** - **c.** Compute the test-statistic and report the value to three decimal places. 4. **Determination of P-Value:** - **d.** Calculate and present the p-value to four decimal places. 5. **Comparison of P-Value and Significance Level:** - **e.** Assess if the p-value is less than or equal to \(\alpha\). 6. **Decision Making:** - **f.** Based on the comparison, make a decision to reject or fail to reject the null hypothesis. 7. **Conclusion:** - **g.** Draw an overall conclusion: - Option 1: At the 5% significance level, there is insufficient evidence to conclude a difference in racial distribution. - Option 2: At the 5% significance level, there is sufficient evidence to conclude a difference in racial distribution. **Conclusion:** This guide will help assess whether there is a significant difference in the racial distribution between students involved in work-study programs and those who are not. Decisions are made based on the computed statistical analyses and relevant hypothesis testing results.
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