There are 2000 households in Happy Valley, distributed across 20 districts. Five

Question

There are 2000 households in Happy Valley, distributed across 20 districts. Five districts were sampled with replacement, with each random draw weighting a district in proportion to the number of households it contains. By luck, no district was selected more than once. Within each selected district, a simple random sample of 10% of the district's households was taken. Let H be the number of households in a district, and let C be the total number of cars owned by residents of those households sampled in the district. The five observed values of (H, C) are (90, 4), (130, 6), (70, 8), (100, 6) and (110, 9) (a) Give an estimate of the total number of cars owned by Happy Valley residents. Report your answer to the nearest integer (b) Give a standard error to accompany your estimate. Report your answer to the nearest integer

Explanation / Answer

Total number of Househols across 5 Districts=500

Sampled population= 50 Households

Estimated Total number of cars=33

Probability of owning a car= 33/50 = 0.66

Applying the same probability to 2000 household, Estimated number of cars across 2000 househols= 2000*0.66=1320

B) Standard error: From the average number of cars per household in the table above, standard error per household=0.29

Standard error across 2000 Household= 2000*0.29= 584

# District Population Cars Sampled Population Probability Estimated cars in District Aveage number of cars per household 1 90 4 9 0.44 40 0.44 2 130 6 13 0.46 60 0.46 3 70 8 7 1.14 80 1.14 4 100 6 10 0.60 60 0.60 5 110 9 11 0.82 90 0.82

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