Question 1200717
**1. Set up Hypotheses**

* **Null Hypothesis (H0):** σ1² = σ2² (The variances of listening times for men and women are equal)
* **Alternative Hypothesis (H1):** σ1² ≠ σ2² (The variances of listening times for men and women are not equal)

**2. Calculate Test Statistic (F-statistic)**

* F = s1² / s2² 
* F = 16² / 15² 
* F = 256 / 225 
* F = 1.138

**3. Determine Degrees of Freedom**

* Degrees of freedom for the numerator (df1) = n1 - 1 = 10 - 1 = 9
* Degrees of freedom for the denominator (df2) = n2 - 1 = 13 - 1 = 12

**4. Find the P-value**

* Using an F-distribution table or statistical software (like R or Python), find the p-value associated with the calculated F-statistic (1.138), df1 = 9, and df2 = 12. 
* **P-value ≈ 0.7724** 

**5. Make a Decision**

* **Significance Level (α) = 0.02**
* **Since the p-value (0.7724) is greater than α (0.02), we fail to reject the null hypothesis.**

**Conclusion**

* At the 0.02 significance level, there is **not enough evidence** to conclude that there is a difference in the variation in listening times for men and women.

**Note:**

* This analysis assumes that the listening times for both men and women are normally distributed. 
* If the normality assumption is not met, other tests like the Levene's test or Bartlett's test might be more appropriate.