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📘 Example: F-Test for Two Variances 🎯 Problem: Two factories produce the same type of product. A quality inspector wants to know if their product weight variances are different. The data: Factory A: Sample size Sample variance Factory B: Sample size Sample variance At a 5% significance level , test whether the variances are significantly different . ✅ Step 1: Set Hypotheses We are testing: (variances are equal) (variances are not equal) ✅ Step 2: Compute F-statistic Use the formula: F = \frac{\text{larger variance}}{\text{smaller variance}} = \frac{20}{10} = 2.00 Let: Numerator df = Denominator df = ✅ Step 3: Find Critical Values We use a two-tailed test at α = 0.05 → Each tail has 0.025. We need: Upper critical value Lower critical value From F-distribution tables: → so F_{0.025,14,11} = \frac{1}{3.21} \approx 0.311 ✅ Step 4: Decision Rule Reject if or Our F = 2.00 → Lies between 0.311 and 3.29 ✅ Step 5: Conclusion ...