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 30 for each such local business venture. For the analysis, he uses a historical (population) standard deviation of $23,300 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¯1x¯1 = $249,000	x¯2x¯2 = $235,700
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 rejectReject H0.At either the 1% significance levels, we (Click to select)cannotcan 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)RejectDo not reject H0.At either the 5% significance levels, we (Click to select)cancannot conclude the mean profitability differs between condominiums and apartment buildings.

Answer 1

a) The correct hypotheses are :

H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

b) The test statistic can be written as

which under H₀ follows a standard normal distribution.

Here,

Now,

The value of the test statistic

P-value

c-1) Since P-value < 0.01, so we reject H₀ at 0.01 level of significance and we can conclude the mean profitability differs between condominiums and apartment buildings.

c-2) Since P-value < 0.05, so we reject H₀ at 0.05 level of significance and we can conclude the mean profitability differs between condominiums and apartment buildings.