Collinsville Construction Company Purchases Steel Rods for Its Projects $\alpha$ = 005,the Appropriate Decision Is ___

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests,Claude Carter,Quality Assurance Manager,has recommended purchasing rods from Redding Rods,Inc.(population 1) ,rather than Stockton Steel (population 2) ,since Redding's rods had less variability in length.Recently,Stockton revised it rod shearing operation,and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes.The results for Redding were s₁² = 0.10 with n₁ = 8,and,for Stockton,the results were s₂² = 0.05 with n₂ = 10.Assume that rod lengths are normally distributed in the population If $\alpha$ = 0.05,the appropriate decision is ___.

A) reject the null hypothesis $\sigma$ ₁²= $\sigma$ ₂²
B) reject the null hypothesis $\sigma$ ₁² < $\sigma$ ₂²
C) do not reject the null hypothesis $\sigma$ ₁²= $\sigma$ ₂²
D) do not reject the null hypothesis $\sigma$ ₁² < $\sigma$ ₂²
E) do nothing