Because of uncertainty in real estate markets, many homeowners are considering remodeling and constructing additions rather than selling, probably the most expensive room in the house to remodel is the kitchen, with an average cost of about $23,400. In terms of resale value, is remodeling the kitchen worth the cost? The following cost and resale figures are published by remodeling magazine for 11 cities. Assume the differences are normally distributed in the population.    City Cost Resale Atlanta $20427 $25163 Boston $27255 $24625 Des Moines $22115 $12600 Kansas City $23256 $24588 Louisville $21877 $19267 Portland $24255 $20150 Raleigh $19852 $22500 Reno $23624 $16667 Ridgewood $25885 $26875 San Francisco $28999 $35333 Tulsa $20836 $16292   Requirements: Use the above data to construct a 99% confidence interval for the difference between cost and added resale value of kitchen remodeling.  At 1% level of significance, is there evidence that the difference between cost and added resale value of kitchen remodeling exist?     Which test statistics is applicable in this case and why?

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Because of uncertainty in real estate markets, many homeowners are considering remodeling and constructing additions rather than selling, probably the most expensive room in the house to remodel is the kitchen, with an average cost of about $23,400. In terms of resale value, is remodeling the kitchen worth the cost? The following cost and resale figures are published by remodeling magazine for 11 cities. Assume the differences are normally distributed in the population.   

City

Cost

Resale

Atlanta

$20427

$25163

Boston

$27255

$24625

Des Moines

$22115

$12600

Kansas City

$23256

$24588

Louisville

$21877

$19267

Portland

$24255

$20150

Raleigh

$19852

$22500

Reno

$23624

$16667

Ridgewood

$25885

$26875

San Francisco

$28999

$35333

Tulsa

$20836

$16292

 

Requirements:

  • Use the above data to construct a 99% confidence interval for the difference between cost and added resale value of kitchen remodeling. 
  • At 1% level of significance, is there evidence that the difference between cost and added resale value of kitchen remodeling exist?    
  • Which test statistics is applicable in this case and why?                                                                   

                                                                                                     

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