Suppose that in past years the average price per square foot

Suppose that in past years the average price per square foot for warehouses in the United States has been $32.28. A national real estate investor wants to determine whether that figure has changed now. The investor hires a researcher who randomly samples 19 warehouses that are for sale across the United States and finds that the mean price per square foot is $31.67, with a standard deviation of $1.29. If the researcher uses a 5% level of significance, what are the appropriate hypotheses? Select one:

1.

A. HO: 32.28 H1: < 32.28

B. HO: = 32.28 H1: 32.28

C. HO: = 31.67 H1: 31.67

D. None of the above answers is correct

2.

what is the value of test statistic?

Select one:

A. 2.06

D. -2.06

E. None of the above answers is correct

3.

what is (are) the critical value(s)?

Select one:

A. 2.101

D. -2.101

E. None of the above answers is correct

4.

what statement should be made about the null and alternative hypothesis based on sample data and significance level?

Select one:

A. fail to reject H_O

B. reject H_O

C. fail to reject H_a

D. reject H_a

E. None of the above answers is correct

5.

what specific conclusion can be drawn about the price for square foot of warehouses in United States?

Select one:

A. the price has not changed

B. the prices has decreased

C. the price has changed

D. the price has not decreased

E. None of the above answers is correct

Solution

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   32.28  
Ha:    u   =/   32.28   [ANSWER]

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2.

Getting the test statistic, as              
              
X = sample mean =    31.67          
uo = hypothesized mean =    32.28          
n = sample size =    19          
s = standard deviation =    1.29          
              
Thus, t = (X - uo) * sqrt(n) / s =    -2.061184772   [ANSWER, OPTION D]

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3.
              
As we can see, this is a    two   tailed test.                      
Thus, getting the critical t,              
df = n - 1 =    18          
tcrit =    +/-2.101 [ANSWER, C]

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4.      
              
As |t| < 2.101, we   FAIL TO REJECT THE NULL HYPOTHESIS.   [OPTION A]

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5.

OPTION A. the price has not changed. [ANSWER]