(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 |
n_{1} = 32 | n_{2} = 32 |
a. Set up the hypotheses to test whether the mean profitability differs between condominiums and apartment buildings.
H_{0}: μ_{1} − μ_{2} = 0; H_{A}: μ_{1} − μ_{2} ≠ 0
H_{0}: μ_{1} − μ_{2} ≥ 0; H_{A}: μ_{1} − μ_{2} < 0
H_{0}: μ_{1} − μ_{2} ≤ 0; H_{A}: μ_{1} − μ_{2} > 0
b. Calculate the value of the test statistic. (Round your answer to 2 decimal places.)
c. Find the p-value.
p-value < 0.01
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?
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
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