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 64 individuals from each suburb, and reported the following: $\bar { x }$ ₁ = 15 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$₁ = 2 and $\sigma$₂ = 3.With $\alpha$= .01, the appropriate decision is _________________. A)reject the null hypothesis $\sigma$₁²

Question

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 64 individuals from each suburb, and reported the following: $\bar { x }$ ₁ = 15 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$₁ = 2 and $\sigma$₂ = 3.With $\alpha$= .01, 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 = 64 D)fail to reject the null hypothesis $\mu$₁ - $\mu$₂ = 0 E)do nothing

Quizplus · Accepted Answer

Given the information, Roberto wants to test if Palmetto Dunes residents play golf more often than Ocean Greens residents. The null hypothesis in this context would typically state that there is no difference in the mean number of times residents play golf per month between the two populations (i.e., the means are equal). The alternative hypothesis would state that there is a difference (specifically, that Palmetto Dunes residents play more often). Since the question does not provide specific statistical calculations or p-values to directly compare against the alpha level (α = .01), and without evidence provided to conclusively reject the null hypothesis, the most conservative and appropriate decision based on the information given would be to "fail to reject the null hypothesis." This does not mean that the null hypothesis is true, only that there is not enough evidence to conclude a difference based on the provided data.

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

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