Your Company Is Evaluating Two Cloud-Based Secured Data Storage Services $\sigma$

Multiple Choice

Your company is evaluating two cloud-based secured data storage services."Pie in the Sky," the newer service, claims its uploading and downloading speeds are faster than the older service, "Cloudy but Steady Skies." You need to make a decision based on published access times for both services at different times and for varying file sizes.To make your decision, you purchase a statistical study, which indicates that average download time for Pie in the Sky is 0.77 sec.per MB and for Cloudy but Steady Skies is 0.84.Assume that n₁ = n₂ = 50, $\sigma$ ₁ = 0.2 and $\sigma$ ₂ = 0.3.With $\alpha$ = .05, the appropriate decision is ______.

A) reject the null hypothesis $\sigma$ ₁² < $\sigma$ ₂²
B) accept the alternate hypothesis $\mu$ ₁ − $\mu$ ₂ $\gt$ 0
C) reject the alternate hypothesis n₁ = n₂ = 50
D) fail to reject the null hypothesis $\mu$ ₁ − $\mu$ ₂ ≤ 0
E) do nothing