Do college majors have any effect on starting salanes after graduation? 350 recent graduates were surveyed about their majors in college and their starting salaries after graduation. Table I below shows the data. Conduct test of independence at the 99% level of confidence. Round to 2 decimal places. Observed Ereguencies Major

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**Title: Analyzing the Impact of College Majors on Starting Salaries**

**Introduction:**
Do college majors have any effect on starting salaries after graduation? In this study, 350 recent graduates were surveyed about their majors in college and their starting salaries after graduation.

**Data Presentation:**

**Table 1: Starting Salaries by College Major**

| Major       | <$50K | $50-69K | $69K+ | TOTAL |
|-------------|-------|---------|-------|-------|
| English     | 20    | 20      | 25    | 65    |
| Engineering | 10    | 35      | 50    | 95    |
| Nursing     |  5    | 15      | 25    | 45    |
| Business    | 15    | 25      | 25    | 65    |
| Psychology  | 10    | 40      | 30    | 80    |
| **TOTAL**   | **60**| **135** | **155**|**350**|

**d. The critical value is:**

**e. We fail to reject the null hypothesis (Write "true" or "false" in the blank):**

**Graph/Diagram Explanation:**
The table above represents the survey data categorized by major and starting salary ranges. Each row corresponds to a major and each column represents a salary range. The total number of graduates surveyed is provided in the "TOTAL" column and row, summing up to 350 graduates.

The purpose of this analysis is to conduct a chi-square test of independence at the 99% confidence level to determine if there is a significant association between college majors and starting salaries.

**Critical Value Calculation:**
To calculate the critical value for the chi-square test, you would typically use a chi-square distribution table and the degrees of freedom (df), which can be determined by the formula: \( (number of rows - 1) \times (number of columns - 1) \). In this case, the degrees of freedom are calculated as \( (5-1) \times (3-1) = 4 \times 2 = 8 \).

**Conclusion:**
After calculating the chi-square statistic and comparing it to the critical value obtained from the chi-square distribution table, you need to decide whether to reject or fail to reject the null hypothesis. If the chi-square statistic
Transcribed Image Text:**Title: Analyzing the Impact of College Majors on Starting Salaries** **Introduction:** Do college majors have any effect on starting salaries after graduation? In this study, 350 recent graduates were surveyed about their majors in college and their starting salaries after graduation. **Data Presentation:** **Table 1: Starting Salaries by College Major** | Major | <$50K | $50-69K | $69K+ | TOTAL | |-------------|-------|---------|-------|-------| | English | 20 | 20 | 25 | 65 | | Engineering | 10 | 35 | 50 | 95 | | Nursing | 5 | 15 | 25 | 45 | | Business | 15 | 25 | 25 | 65 | | Psychology | 10 | 40 | 30 | 80 | | **TOTAL** | **60**| **135** | **155**|**350**| **d. The critical value is:** **e. We fail to reject the null hypothesis (Write "true" or "false" in the blank):** **Graph/Diagram Explanation:** The table above represents the survey data categorized by major and starting salary ranges. Each row corresponds to a major and each column represents a salary range. The total number of graduates surveyed is provided in the "TOTAL" column and row, summing up to 350 graduates. The purpose of this analysis is to conduct a chi-square test of independence at the 99% confidence level to determine if there is a significant association between college majors and starting salaries. **Critical Value Calculation:** To calculate the critical value for the chi-square test, you would typically use a chi-square distribution table and the degrees of freedom (df), which can be determined by the formula: \( (number of rows - 1) \times (number of columns - 1) \). In this case, the degrees of freedom are calculated as \( (5-1) \times (3-1) = 4 \times 2 = 8 \). **Conclusion:** After calculating the chi-square statistic and comparing it to the critical value obtained from the chi-square distribution table, you need to decide whether to reject or fail to reject the null hypothesis. If the chi-square statistic
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