plz use two stage cluster to do this question A sociologist wants to investigate

Question

plz use two stage cluster to do this question

A sociologist wants to investigate the number of retired people living in a certain city. She decides to sample city blocks and then sample households within blocks. Four blocks are randomly selected from the 300 in the city, with the following results. (a) Estimate the total number of retired residents in the city. (b) Give the standard error of this estimate. (c) Estimate the mean number of retired residents per household. (d) Give a stndard error for this estimate.

Explanation / Answer

(a)

Total number of blocks = 300

Calculating total number of households in the city,

Mean number of households in 4 blocks = 18+14+9+12 = 53/4 = 13.25

Hence, number of households in 300 blocks = 13.25 * 300 = 3975

Total number of retired residents in 12 households selected = 3.9

Therefore, number of retired residents in the city = ( 3975/12 ) * 3.9 = 1292

(c) Mean number of retired residents per household = total mean of the households sampled which is

equal to 3.9

block households households sampled retired residents mean 1 18 3 1,0,2 1 2 14 3 0,3,0 1 3 9 3 1,1,2 1.3 4 12 3 0,1,1 0.6

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