Question

A civil engineer aims to estimate the total number of potholes in a city so that a re-development budget can be drawn up. It is not possible to survey the whole city for practical reasons. Therefore, the city is split into a grid of 500 areas of size 1km2. The engineer randomly selects 50 of these areas and counts the number of potholes; a total 238 potholes are counted. Assuming that the potholes are geographically distributed according to a Poisson distribution, construct a 95% confidence interval for the total number of potholes in the whole city.

Answer 1

Mean/Expected number of events of interest: λ =   (238/50)*500

= 2380

std dev = √λ =    48.78524367

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   499          
't value='   tα/2=   1.9647   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   48.7852   / √   500   =   2.181742
margin of error , E=t*SE =   1.9647   *   2.18174   =   4.286533
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    2380.00   -   4.286533   =   2375.713467
Interval Upper Limit = x̅ + E =    2380.00   -   4.286533   =   2384.286533
95%   confidence interval is (   2375.71   < µ <   2384.29   )

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