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 20% of purchases were for​ condominiums, 25% 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 is shown in the table below. What is the standardized residual associated with townhouses? (Round to two decimal places.)

Type of Property & Frequency:

Condos =89, Townhouses = 121, Homes = 78, Commercial = 25, Land = 12

Answer 1

Applying chi square data:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.200	89.00	65.00	2.98	8.862
2	0.250	121.00	81.25	4.41	19.447
3	0.400	78.00	130.00	-4.56	20.800
4	0.100	25.00	32.50	-1.32	1.731
5	0.0500	12.00	16.25	-1.05	1.112
total	1.000	325	325		51.951

standardized residual associated with townhouses =4.41