Question 1193978
**1. Set up Hypotheses**

* **Null Hypothesis (H0):** Absenteeism is evenly distributed throughout the workweek. 
* **Alternative Hypothesis (H1):** Absenteeism is not evenly distributed throughout the workweek.

**2. Calculate Expected Frequencies**

* **Total Absences:** 12 + 9 + 11 + 10 + 9 + 9 = 60 
* **Expected Absences per Day (under the null hypothesis):** 60 absences / 6 days = 10 absences/day

* **Create a table:**

| Day       | Observed (O) | Expected (E) | (O - E)² | (O - E)² / E |
|-----------|-------------|-------------|---------|-------------|
| Monday    | 12          | 10          | 4       | 0.4        |
| Tuesday   | 9           | 10          | 1       | 0.1        |
| Wednesday | 11          | 10          | 1       | 0.1        |
| Thursday  | 10          | 10          | 0       | 0          |
| Friday    | 9           | 10          | 1       | 0.1        |
| Saturday  | 9           | 10          | 1       | 0.1        |
| **Total** | 60          | 60          |   | **0.8**      |

**3. Calculate the Chi-Square Test Statistic**

* χ² = Σ [(O - E)² / E] = 0.8

**4. Determine Degrees of Freedom**

* Degrees of Freedom (df) = Number of categories - 1 = 6 - 1 = 5

**5. Find the Critical Value**

* Using a chi-square distribution table, find the critical value for α = 0.01 and df = 5. 
* The critical value is approximately 15.086.

**6. Make a Decision**

* **Compare the calculated chi-square statistic to the critical value:**
    * 0.8 < 15.086

* **Decision:** Since the calculated chi-square statistic (0.8) is less than the critical value (15.086), we **fail to reject the null hypothesis**.

**7. Conclusion**

* There is **not enough evidence** at the 0.01 level of significance to conclude that absenteeism is not evenly distributed throughout the workweek. 

**Interpretation for the Human Resources Director:**

* This analysis suggests that there is no significant evidence to indicate that absenteeism is more prevalent on any particular day of the week. 
* The observed variations in absenteeism across the days could be due to random chance. 
* The HR director may need to investigate other factors that might be contributing to absenteeism, such as employee health, work-life balance, or job satisfaction.

**Note:**

* This analysis assumes that the data meets the assumptions of the chi-square test, such as expected frequencies being sufficiently large (generally, expected frequencies should be greater than 5).

This analysis provides a basic framework for conducting a chi-square goodness-of-fit test.