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 31 individuals from each suburb, and reported the following: 01 = 15 times per month and 22 = 14 times per month. Assume that $1 = 2 and 82 = 3, and 01 +02. What is the conclusion of this test? Based on this sample, at 1% significance level, there is not sufficient evidence to conclude that Palmetto Dunes residents play golf more often than Ocean Greens residents. Based on this sample, at 100% significance level, there is not sufficient evidence to conclude that Palmetto Dunes residents play golf more often than Ocean Greens residents. Based on this sample, at 1% significance level, there is sufficient evidence to conclude that Palmetto Dunes residents play golf more often than Ocean Greens residents. Based on this sample, at 1% significance level, there is sufficient evidence to conclude that Palmetto Dunes residents play golf less often than Ocean Greens residents. This test is inconclusive.

Answer 1

We have to test (Right tailed T-test)

$H_0:\mu _1-\mu _2=0\\ H_1:\mu _1-\mu _2 > 0$

The sample means are $\overline{x_1}=15, \overline{x_2}=14$ . The sample standard deviations are . Sample sizes are $n_1=31,n_2=31$ . Degrees of freedom $n_1+n_2-2=60$ .

We use T distribution since the population standard deviations are not known.

The test statistic is

$t=\left (\overline{x_1}-\overline{x_2} \right )/\sqrt{\frac{s _1^2}{n_1}+\frac{s _2^2}{n_2}}\\ t=\left (15-14 \right )/\sqrt{\frac{2^2}{31}+\frac{3^2}{31}}\\ t=1.54422$

The P-value is

$\textup{p-value}=P\left ( T>1.54422 \right )\\ \textup{p-value}=\Phi _T\left (T<-1.54422\right )\\ \textup{p-value}={\color{Blue} 0.064}$

Sinc the P-value $\textup{P-value} = 0.064>0.01$ , we retain retain the null hypothesis

Conclusion is Fail to Reject H0.

The data does not suggest at 1% significance level there is no sufficient evidence to conclude that ...........................

First choice is correct.