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Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich
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Square footage of new California homes. The average size

Chapter 7, Problem 102E

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QUESTION:

Problem 102E

Square footage of new California homes. The average size of single-family homes built in the United States is 2,390 square feet (Statistical Abstract of the United States, 2011). A random sample of 100 new homes sold in California yielded the following size information:  = 2,507 square feet and s = 257 square feet.

a. Assume the average size of U.S. homes is known with certainty. Do the sample data provide sufficient evidence to conclude that the mean size of California homes built exceeds the national average? Test using  = .01.

b. Suppose the actual mean size of new California homes was 2,490 square feet. What is the power of the test in part a to detect this 100-square-foot difference?

c. If the California mean were actually 2,440 square feet, what is the power of the test in part a to detect this 50-square-foot difference?

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QUESTION:

Problem 102E

Square footage of new California homes. The average size of single-family homes built in the United States is 2,390 square feet (Statistical Abstract of the United States, 2011). A random sample of 100 new homes sold in California yielded the following size information:  = 2,507 square feet and s = 257 square feet.

a. Assume the average size of U.S. homes is known with certainty. Do the sample data provide sufficient evidence to conclude that the mean size of California homes built exceeds the national average? Test using  = .01.

b. Suppose the actual mean size of new California homes was 2,490 square feet. What is the power of the test in part a to detect this 100-square-foot difference?

c. If the California mean were actually 2,440 square feet, what is the power of the test in part a to detect this 50-square-foot difference?

ANSWER:

Solution:

Step 1 of 4:

The average size of single-family homes built in the United states is 2,390 square feet.

A random sample of 100 new homes sold in california yielded the size information: =2,507 square feet and s= 257 square feet.

 

We have to find,

 (a) Do the sample data provide sufficient evidence to conclude that the mean size of  California homes built exceeds the national average, if

(b) The power of the test in part a to detect this 100-square-foot difference, if the actual mean size of new California homes was 2,490 square feet,

  (c) The power of the test in part a to detect this 50-square-foot difference, if the California mean were actually 2,440 square feet.

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