2. 124 points) A truck rental company has a feet of 80 trucks. Each truck has 8
ID: 3131592 • Letter: 2
Question
2. 124 points) A truck rental company has a feet of 80 trucks. Each truck has 8 tires. There are a total of 640 tires. The company seeks to estimate the total number of tires that are defective. The company picks a simple random sample without replacement of 5 trucks from the 80 trucks. For each sampled vehicle, the number of defective tires is recorded. The following are the sample results: Vehicle truckl truck2 truck3 truck4 truck5 Number of defective tires 23 03 (1) (8 potnts] What is a sampling unit? How many sampling units are there? (2) [8 points) Estimate the number of tires that are defective.Explanation / Answer
(a)
Definnition of sampling unit :
A sampling unit is one of the units into which an aggregate is divided for the purpose of sampling, each unit being regarded as individual and indivisible when the selection is made . Thus here we have population 80 trucks. Each truck is a unit of the population. But when we select 5 truck randomly out of the 80 truck to estimate some population parameter( here no of defective tyres of 80*8=640 tyres) then each of the 5 randomly chosen truck is called observation unit. and total 5*8 =40 tyres that has been chosen out of 640 tyres is called sampling unit as it is indivisible.
Here as we are selecting 5 trucks, so there are 5*8 =40 tyres that has been sampled, so the number of sampling unit is 40.
(b) from the sample the total number of defective tyres = (2+1+3+0+3) = 9. and total no of sampling unit =40. So the sample proportion of defective tyres = 9/40 . Now we know for SRS population proportion is unbiased estimate of sample proportion, so an estimate of the number of defective tyres in 640 tyres = 640*9/40 = 144.
the answer is 144.
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