
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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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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