A certain city has 80 blocks. We select a sample of 4 blocks using simple random...

 

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A certain city has 80 blocks. We select a sample of 4 blocks using simple random sampling without replacement. From each block 5 households were drawn randomly without replacement. The number of videocassette recorders (VCR's) in each household were recorded. The data is as follows: Sample block Number of households 1 2 3 4 100 150 80 100 Number of VCR's in sample households 1 1 0 1 2 2 2 1 0 2 M 1 1 0 2 4 1 1 1 1 5 0 2 1 1 Calculate an unbiased estimate of the total number of VCR's in the city. Question 2 [14 marks] (a) Describe briefly how the stratified sampling and cluster sampling techniques differ with respect to the variance of the elements within their respective samples. [2+2 marks] (b) Suppose that in a population with N = 6 and L = 2 the values of yni, i = 1,2,3 are 0, 1, 2 in stratum 1 and 4, 6, 11 in stratum 2. A sample of size n = 4 is to be taken. Show that the optimum nunder Neyman allocation, when rounded to the nearest integers, are n, 1 in stratum 1 and n₁ = 3 in stratum 2. [10 marks] [18 marks] A certain city has 80 blocks. We select a sample of 4 blocks using simple random sampling without replacement. From each block 5 households were drawn randomly without replacement. The number of videocassette recorders (VCR's) in each household were recorded. The data is as follows: Sample block Number of households 1 2 3 4 100 150 80 100 Number of VCR's in sample households 1 1 0 1 2 2 2 1 0 2 M 1 1 0 2 4 1 1 1 1 5 0 2 1 1 Calculate an unbiased estimate of the total number of VCR's in the city. Question 2 [14 marks] (a) Describe briefly how the stratified sampling and cluster sampling techniques differ with respect to the variance of the elements within their respective samples. [2+2 marks] (b) Suppose that in a population with N = 6 and L = 2 the values of yni, i = 1,2,3 are 0, 1, 2 in stratum 1 and 4, 6, 11 in stratum 2. A sample of size n = 4 is to be taken. Show that the optimum nunder Neyman allocation, when rounded to the nearest integers, are n, 1 in stratum 1 and n₁ = 3 in stratum 2. [10 marks] [18 marks]