Collinsville Construction Company Purchases Steel Rods for Its Projects $\sigma$ ₁ ²

Multiple Choice

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc.(population 1) , and switching to Stockton Steel (population 2) , since Stockton's rods had less variability in length.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.Claude's null hypothesis is ________________.

A) $\sigma$ ₁ ² $\le$ $\sigma$ ₂ ²
B) $\sigma$ ₁ ² $\neq$$\sigma$ ₂ ²
C) $\sigma$ ₁ ² $\gt$ $\sigma$ ₂ ²
D) $\sigma$ ₁ ² $\lt$$\sigma$ ₂ ²
E) s ₁ ² $\lt$ s ₂ ²