To compare the variations in weight of four breeds of dogs, researchers took independent random samples of sizes n₁ = 8, n₂ = 10, n₃ = 6, and n₄ = 8, and got σ²₁ = 16, σ²₂ = 25, σ²₃ = 12, and σ²₄ = 24. Assuming that the populations sampled are normal, use the formula of part (b) of Exercise 12.25 to calculate –2 · ln λ and test the null hypothesis σ²₁ = σ²₂ = σ²₃ = σ²₄ at the 0.05 level of significance. Explain why the number of degrees of freedom for this approximate chi-square test is 3.