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 30 for each such local business venture. For the analysis, he uses a historical (population) standard deviation of $21,900 for condominiums and $20,000 for apartment buildings. Use Table 1.

Sample 1 represents condominiums and Sample 2 represents apartment buildings.

Condominiums	Apartment Buildings
x⎯⎯1x¯1 = $249,000	x⎯⎯2x¯2 = $236,300
n1 = 30	n2 = 30

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

(Click to select)  Do not reject  Reject   H0.At either the 1% significance levels, we  (Click to select)  cannot  can   conclude the mean profitability differs between condominiums and apartment buildings.

c-2.	At the 5% significance level, what is the conclusion to the test?

(Click to select)  Do not reject  Reject   H0.At either the 5% significance levels, we  (Click to select)  cannot  can   conclude the mean profitability differs between condominiums and apartment buildings.

Answer 1

The statistical software output for this problem is:

Hence,

a) Hypotheses: Option A is correct.

b) Test statistic = 2.35

p - Value = 0.019

c - 1) Do not reject; Cannot

c - 2) Reject; Can