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 32 for each such local business ventures. For the analysis, he uses a historical (population) standard deviation of $22,900 for condominiums and $19,700 for apartment buildings. (You may find it useful to reference the appropriate table: z table or t table)

Sample 1 represents condominiums and Sample 2 represents apartment buildings.

Condominiums	Apartment Buildings
x⎯⎯1x¯1 = $249,700	x⎯⎯2x¯2 = $236,400
n1 = 32	n2 = 32

a. Set up the hypotheses to test whether the mean profitability differs between condominiums and apartment buildings.

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

b. Calculate the value of the test statistic. (Round your answer to 2 decimal places.)

c. Find the p-value.

• 0.01 p-value < 0.025

• p-value < 0.01

• p-value 0.10
• 0.05 p-value < 0.10
• 0.025 p-value < 0.05

d-1. At the 5% significance level, what is the conclusion to the test?

d-2. At the 10% significance level, what is the conclusion to the test?

Answer 1

The statistical software output for this problem is:

On the basis of above output:

a) H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0

b) Test statistic = 2.49

c) 0.01 < p < 0.025

d - 1) Reject Ho

d - 2) Reject Ho