Question 1193670
**A. 2x2 Table**

|        | Survived | Died | Row Total |
|---------|----------|------|----------|
| Active  | 30       | 10   | 40        |
| Inactive| 70       | 90   | 160       |
| Column Total| 100      | 100   | 200       |

**Expected Frequencies:**

|        | Survived | Died | Row Total |
|---------|----------|------|----------|
| Active  | 20       | 20   | 40        |
| Inactive| 80       | 80   | 160       |
| Column Total| 100      | 100   | 200       |

**Calculation of Expected Frequencies (for Active/Survived cell):** 

* (Row Total for Active * Column Total for Survived) / Grand Total 
* (40 * 100) / 200 = 20

**B. Hypothesis Testing**

* **H0 (Null Hypothesis):** There is no association between physical activity and mortality from a heart attack. 
* **H1 (Alternative Hypothesis):** There is an association between physical activity and mortality from a heart attack.

**Chi-Square Test Statistic:**

* χ² = Σ [(O - E)² / E] 
    * Where:
        * O = Observed frequency
        * E = Expected frequency

* Calculate for each cell:
    * (30 - 20)² / 20 = 5
    * (10 - 20)² / 20 = 5
    * (70 - 80)² / 80 = 1.25
    * (90 - 80)² / 80 = 1.25

* Sum the values: χ² = 5 + 5 + 1.25 + 1.25 = 12.5

**Degrees of Freedom (df):**

* (Number of rows - 1) * (Number of columns - 1) = (2 - 1) * (2 - 1) = 1

* **Critical Value:** 
    * Using a chi-square distribution table with df = 1 and α = 0.05 (common significance level), the critical value is 3.841.

**Decision:**

* Since the calculated chi-square statistic (12.5) is greater than the critical value (3.841), we reject the null hypothesis.

**C. Conclusion**

* There is sufficient evidence at the 0.05 level of significance to conclude that there is an association between physical activity and mortality from a heart attack. 
* The data suggests that physically active individuals are less likely to die from a heart attack.

**Note:**

* This analysis provides a basic framework for conducting a chi-square test for independence. 
* Further analysis and consideration of other factors could provide a more comprehensive understanding of the relationship between physical activity and heart health.