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

The standardized residual for Townhouses can be calculated using the formula $\frac{(observed - expected)}{\sqrt{expected}}$. The expected frequency for Townhouses, given the historical distribution of 30%, is $325 \times 0.30 = 97.5$. The observed frequency is 121. Thus, the standardized residual is $\frac{(121 - 97.5)}{\sqrt{97.5}} \approx 2.38$.

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