A real estate agency, located in a metropolitan area in the northeastern U.S., kept data on the various types of properties purchased in the area.Historically, 15% of purchases
Were for condominiums, 30% were for townhouses, 40% for single family homes, 10%
For commercial properties and 5% for land.With changing demographics, the agency
Wondered if the current distribution matches the historical distribution.Recent data
Showed the following: What is the standardized residual associated with Townhouses?
A)23.5
B)4.85
C)10.86
D)2.38
E)Not enough information given to calculate.

Question

A real estate agency, located in a metropolitan area in the northeastern U.S., kept data on the various types of properties purchased in the area.Historically, 15% of purchases
Were for condominiums, 30% were for townhouses, 40% for single family homes, 10%
For commercial properties and 5% for land.With changing demographics, the agency
Wondered if the current distribution matches the historical distribution.Recent data
Showed the following:  What is the standardized residual associated with Townhouses?
A)23.5 
B)4.85 
C)10.86 
D)2.38 
E)Not enough information given to calculate.

Quizplus · Accepted Answer

To find the standardized residual for townhouses, we first calculate the expected frequency for townhouses in the recent data:
Expected frequency = Total sample size * Historical proportion for townhouses
Expected frequency = 780 * 0.3 = 234

Then we can calculate the residual for townhouses:
Residual = Observed frequency - Expected frequency
Residual = 250 - 234 = 16

To calculate the standardized residual, we divide the residual by the square root of the expected frequency:
Standardized residual = Residual / sqrt(Expected frequency)
Standardized residual = 16 / sqrt(234)
Standardized residual = 2.38

Therefore, the answer is D) 2.38.

A Real Estate Agency, Located in a Metropolitan Area in the Northeastern