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 venture. For the analysis, he uses a historical (population) standard deviation of $21,900 for condominiums and $19,600 for apartment buildings. Use Table 1. Sample 1 represents condominiums and Sample 2 represents apartment buildings. Condominiums Apartment Buildings x¯1 = $252,000 x¯2 = $235,600 n1 = 34 n2 = 34 a. Set up the hypotheses to test whether the mean profitability differs between condominiums and apartment buildings. H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0 H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0 H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0 b. Compute the value of the test statistic and the corresponding p-value. (Round "test statistic" value to 2 decimal places and "p-value" to 3 decimal places.) Test statistic p-value c-1. At the 5% significance level, what is the conclusion to the test? H0. At either the 5% significance levels, we conclude the mean profitability differs between condominiums and apartment buildings. c-2. At the 10% significance level, what is the conclusion to the test? H0. At either the 10% significance levels, we conclude the mean profitability differs between condominiums and apartment buildings.

Answer 1

H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0

b)

std error σx1-x2=√(σ21/n1+σ22/n2)    =	5040.337
test stat z =(x1-x2-Δo)/σx1-x2     =	3.25

p value =0.001

c-1)

reject Ho: At either the 5% significance levels, we conclude the mean profitability differs between condominiums and apartment buildings.
c-2)

reject Ho: At either the 10% significance levels, we conclude the mean profitability differs between condominiums and apartment buildings.