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 34 for each such local business venture. For the analysis, he uses a historical (population) standard deviation of $21,500 for condominiums and $19,500 for apartment buildings. Use Table 1. |
Sample 1 represents condominiums and Sample 2 represents apartment buildings. |
Condominiums | Apartment Buildings |
x⎯⎯1x¯1 = $248,300 | x⎯⎯2x¯2 = $235,300 |
n1 = 34 | n2 = 34 |
a. |
Set up the hypotheses to test whether the mean profitability differs between condominiums and apartment buildings. |
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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 10% significance level, what is the conclusion to the test? |
(Click to select)RejectDo not reject H0.At either the 10% significance levels, we (Click to select)cancannot conclude the mean profitability differs between condominiums and apartment buildings. |
c-2. |
At the 1% significance level, what is the conclusion to the test? |
(Click to select)RejectDo not reject H0.At either the 1% significance levels, we (Click to select)cancannot conclude the mean profitability differs between condominiums and apartment buildings. |
The statistical software output for this problem is:
Hence,
a) Hypotheses:
H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0
b) Test statistic = 2.61
P - value = 0.009
c - 1) Reject; can
c - 2) Reject; can
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