A real estateagency,located in a metropolitan area in the northeasternU.S,kept d

Question

A real estateagency,located in a metropolitan area in the northeasternU.S,kept data on the various types of properties purchased in the area.Historically,15% of purchases were forcondominiums, 30% were or own houses. 40% for single am yhomes 10% for commercial properties and or and th ch ging emographics, hea en wondered if the current distribution matches the historical distribution. Recent data showed the following table below. What is the standardized residual associated with Townhouses? Type of Property Condo Townhouse Homes Commercial Land 78 -25 12 89 Frequency A. 10.86 B. 2.38 D. 23.5

Explanation / Answer

right choice is C. 1.77

standardized residual=(O-E)/sqrt(E)

O=observed frequency,

E=expected frequency=n*p

total frequency=n=316

so for standard residual for town house=(O-E)/sqrt(E)=(112-94.8)/sqrt(94.8)=1.77

observe(O) proportion (p) Expected(E) (O-E) (O-E)/sqrt(E) condo 89 0.15 47.4 41.6 6.04 town 112 0.30 94.8 17.2 1.77 homes 78 0.40 126.4 -48.4 -4.30 commercial 25 0.10 31.6 -6.6 -1.17 land 12 0.05 15.8 -3.8 -0.96 total 316 1 316 -3.6E-15 1.37

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