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 $21,900 for condominiums and $19,900 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 = $249,000	x⎯⎯2x¯2 = $235,200
n1 = 32	n2 = 32

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

• A.) H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• B.) H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• C.)   H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

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

test statistic: ____

c. Find the p-value.

• A.) /p-value < 0.01

• B.) p-value   0.10
• C.) 0.05  p-value < 0.10
• D.) 0.025  p-value < 0.05
• E.) 0.01  p-value < 0.025

d-1. At the 10% significance level, what is the conclusion to the test?

	( REJECT / DO NOT REJECT ) H0. At the 10% significance levels, we		( CAN / CANNOT ) conclude the
mean profitability differs between condominiums and apartment buildings.

Answer 1