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: $$\begin{array} { l | c | c | c | c | c }
\text { Type of Property } & \text { Condos } & \text { Townhouses } & \text { Homes } & \text { Commercial } & \text { Land } \
\hline \text { Frequency } & 89 & 121 & 78 & 25 & 12
\end{array}$$ 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: $$\begin{array} { l | c | c | c | c | c } 
\text { Type of Property } & \text { Condos } & \text { Townhouses } & \text { Homes } & \text { Commercial } & \text { Land } \
\hline \text { Frequency } & 89 & 121 & 78 & 25 & 12
\end{array}$$ 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 calculate the standardized residual, we need to first calculate the expected frequency for each type of property based on the historical distribution. We can do this by multiplying the total number of purchases (325) by the historical percentage for each type of property.

Condos: 0.15 x 325 = 48.75
Townhouses: 0.30 x 325 = 97.5
Homes: 0.40 x 325 = 130
Commercial: 0.10 x 325 = 32.5
Land: 0.05 x 325 = 16.25

We can then calculate the expected frequency for townhouses by subtracting the historical percentage from the observed percentage and multiplying by the total number of purchases.

Expected frequency for townhouses = (0.30 - 121/325) x 325 = 92.65

To calculate the standardized residual for townhouses, we use the formula:

Standardized residual = (observed frequency - expected frequency) / square root(expected frequency)

For townhouses, the observed frequency is 121 and the expected frequency is 92.65. Plugging these values into the formula, we get:

Standardized residual = (121 - 92.65) / square root(92.65) = 2.38

Therefore, the answer is D) 2.38.

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