Question

An entrepreneur owns some land that he wishes to develop. He identifies two development options: build...

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.

H0: μ1μ2 = 0; HA: μ1μ2 ≠ 0
H0: μ1μ2 ≥ 0; HA: μ1μ2 < 0
H0: μ1μ2 ≤ 0; HA: μ1μ2 > 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 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.

Homework Answers

Answer #1

The statistical software output for this problem is:

Hence,

a) Hypotheses:

H0: μ1μ2 = 0; HA: μ1μ2 ≠ 0

b) Test statistic = 2.61

P - value = 0.009

c - 1) Reject; can

c - 2) Reject; can

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