Question

(Round all intermediate calculations to at least 4 decimal places.)

An entrepreneur owns some land that he wishes to develop. He identifies two development options: build condominiums or build apartment buildings. Accordingly, he reviews public records and derives the following summary measures concerning annual profitability based on a random sample of 34 for each such local business ventures. For the analysis, he uses a historical (population) standard deviation of $21,700 for condominiums and $19,700 for apartment buildings.  

Sample 1 represents condominiums and Sample 2 represents apartment buildings

Condominiums $251,600 Apartment Buildings 2$235,600 n1 = 34 n2 = 34 a. Set up the hypotheses to test whether the mean profitability differs between condominiums and apartment buildings b. Calculate the value of the test statistic. (Round your answer to 2 decimal places.) Test statistic

At the 1% significance level, what is the conclusion to the test?

At the 5% significance level, what is the conclusion to the test?

Answer 1

a) Let Hi and t2 be the popul ati on means and let x, and x2 be the means of the respective samples. From the given inform ati on Samplel: » 34 x 251,600 s 21,700 Sample2: nうー34 x, = 235, 600, s, = 19,700 The level of significance is α-005 Step1: State the null and alternative hypotheses The null and alternative hypotheses are, respectively We need to use two-tailed test Ho : μ,-/4 (The two population means are equal) Hı : M 14, (The population mean μ is not equal to 14, Step 2: Select the distributi on to use Here, the two samples are independent, G and C5 are unknown but equal, and the sample sizes are sm all but both populations are normally distributed. Hence, all conditions are sati sfied. Consequently, we will use the t distribution Step3. Determine the rejection and non-rejection regions The sign in the alternative hypothesis indicates that the test is two-tailed. The significance level is 0.05 From the t distribution table, the critical value of t for df 66 and 0.05 area in the right-tail of the t distributi on is 1.996564 From the t distribution table, the critical value of t for df 66 and 0.05 area in the left-tail of the t distributi on is -1.996564

Step 4: Calcul ate the value of the t-test stati sti c The value of the test stati stic t for x,- x2 is computed as follows -1) 87(n-1) S- (34-1)470890000 (34-1)388090000 34 +34-2 33(470890000) +33(388090000) 15539370000 +12806970000 28346340000 V429490000 = 2072414051 s, 20724.14051 20724.1405134 34 = 20724.14051 0.0294 11765+0.029411765 = 20724, 1405N0, 058823529 20724.14051(0.242535625) = 5026.342373 ら--= 5026.342373 The formula for calculating the t-statistic is 지-ろ)-(4-4) 一期 (251600-235600)-(0) 5026.342373 16000 5026.342373 3.183229 t 3.183229 Con clusion. At the 5% significance le veI Since, the test statistic is H-3 183229 > toos.เ4-1 .996564 we reject the null hypothesis Ho Hence, there is sufficient evi dence to conclude that the mean profitability differs between the condominiums and apartment buildings Conclusion: At the 1% significance level Since, the test stati stic is k3.183229too 2652394. We reject the null hypothesis Ho Hence, there is sufficient evidence to conclude that the mean profitability differs between the condominiums and apartment buildings