1. **Problem Statement:** Suppose we have two independent samples from two different populations. The first sample has variance $s_1^2 = 16$ with sample size $n_1 = 25$, and the second sample has variance $s_2^2 = 9$ with sample size $n_2 = 20$. Find the ratio of the two variances and interpret the result. 2. **Formula and Explanation:** The ratio of two sample variances is given by: $$ F = \frac{s_1^2}{s_2^2} $$ This ratio is often used in hypothesis testing (like the F-test) to compare the variability of two populations. A ratio greater than 1 indicates that the first sample has greater variance than the second. 3. **Calculation:** Substitute the given values: $$ F = \frac{16}{9} $$ Simplify the fraction: $$ F = 1.777\ldots $$ 4. **Interpretation:** The ratio $F \approx 1.78$ means the variance of the first sample is about 1.78 times the variance of the second sample. This suggests the first population is more variable than the second. **Final answer:** $$ \boxed{\frac{s_1^2}{s_2^2} = \frac{16}{9} \approx 1.78} $$