1. The city of Smalltown wishes to estimate the average yearly maintenance costs
ID: 3341187 • Letter: 1
Question
1. The city of Smalltown wishes to estimate the average yearly maintenance costs for owner-occupied single family houses. The city council decides to take a simple random sample of 8 such houses on the east side of the tracks, and a simple random sample of 8 houses on the west side of the tracks. The homeowners of each of the 16 houses are interviewed and maintenance costs for last year are determined. The costs are in the table below. For each area of Smalltown, the sample mean and the sample variance of the eight numbers are given. Further, the city council tells you that there are 500 houses in Smalltown, with 100 on the West side and 400 on the East side. East side 237 West side 405 582 1509 234 1393 923 781 573 800 (a) Estimate the average yearly main- tenance costs for owner-occupied single family houses in Smalltown, and find a bound for the error of estimation. (30 pts) 256 406 160 242 236 81 average variance 206465 230 8435Explanation / Answer
A>
Given The Sample Means( Avg. maintenance cost ) for East Side and West Side =230 & 800 Respectively
Total number of houses on East and West Side are 400 & 100 respectively.
Estimated Avg. yearly maintenance cost for the Small town = Weighted Avg of East Side and West Side
Weighted Avg= (N1*230+ N2*800)/(N1+N2)
Where N1= 400 and N2=100
So the averageyearly maintenace costs = ( 400*230+100*800)/(400+100)= 344
B> Computing the sample Size for which the bound of error estimation =$40
Sqrt( Var1/(n-1)- Sqrt (var2/n-1)= 40
Var1 is variance of West side & Var2 Variance of east Side
n= Number to be sampled
Sqrt (n-1)= ( Sqrt Var1- Sqrt var2)/40
n-1= [( Sqrt(206465)-Sqrt(8435))/40]^2
So n= 83
Sample Size= 83
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