Golf Course Designer Roberto Langabeer Is Evaluating Two Sites, Palmetto $\bar { x }$

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course.He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2) .Roberto commissions a market survey to test this hypothesis.The market researcher used a random sample of individuals from each suburb, and reported the following: $\bar { x }$ ₁ = 16 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$ ₁ = 4 and $\sigma$ ₂ = 3.With $\alpha$ = .01, the appropriate decision is _____________.

A) do nothing
B) reject the null hypothesis $\mu$ ₁ < $\mu$ ₂
C) accept the alternate hypothesis $\mu$ ₁- $\mu$ ₂ $\gt$ 0
D) reject the alternate hypothesis n₁ = n₂ = 64
E) do not reject the null hypothesis $\mu$ ₁ - $\mu$ ₂ = 0