Question

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 33 for each such local business ventures. For the analysis, he uses a historical (population) standard deviation of $23,000 for condominiums and $20,000 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 = $244,700	x¯2x¯2 = $235,600
n1 = 33	n2 = 33

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

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

b)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(529000000/33 + 400000000/33)
sp = 5305.8001

Test statistic,
z = (x1bar - x2bar)/sp
z = (244700 - 235600)/5305.8001
z = 1.72

d1)

P-value Approach
P-value = 0.0854
As P-value >= 0.05, fail to reject null hypothesis.

d2)

P-value Approach
P-value = 0.0854
As P-value < 0.1, reject null hypothesis.