A rental car company wants to estimate the proportion of unsafe tires on their 1

Question

A rental car company wants to estimate the proportion of unsafe tires on their 175 cars. It is impractical to select a simple random sample of tires from the fleet, so a cluster sampling design is used, where each car is a c An SRS of 30 cars is selected and the numbers of unsafe tires^2 are given below. 2, 4, 0, 1, 2, 0, 4, 1, 3, 1, 2, 0, 1, 1, 2, 2, 4, 1, 0, 0, 3, 1, 2, 2, 1, 2, 2, 1, 0, 0 Estimate the proportion of unsafe tires in the fleet and provide an approximate standard error for your estimator.

Explanation / Answer

for 30 given SRS of Cars total sum of unsafe tyres = 45

so mean number of tyres unsafe = 45/30 = 1.5 per car.

Proportion of unsafe tires in the fleet = 1.5/4 = 0.375

standard error of the estimator = Standard Error of proportion * sqrt [ (N-n)/ (N-1) ]

= sqrt [ p* (1-p*) (N-n)/ n(N-1) ] = sqrt [ (0.375 * 0.625 * (175 -30))/ (30 * (175-1)) ]

= sqrt [ 33.9843/ 5220] = 0.080

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