A sample survey questions

MURANG’A UNIVERSITY OF TECHNOLOGY

AMS 201 SAMPLE SURVEY CAT 3

Attempt the numerical problems in R software

1.Following are the quantities of yield of rice (in million metric tons) in 44

countries:

.04, 2.80, 21.90, .04, 2.63, 19.52, .27, .06, 2.60, 1.10, 15.60, 4.50, .08, .16, .09,

.15, 2.31, 15.40, 2.18, 14.58, .11, .30, 9.02, 4.50, .11, .40, 5.6, 8.30, 6.17, 7.86,

1.10, 1.90, 1.40, 1.76, 1.90, .42, .46, 1.06, .86, .99, .97, .47, .52, .48

Treating this as a population,

(i) divide them into suitable numbers of strata.

(ii) find the required number of units to be drawn in the sample if the population

coefficient of variation does not exceed 0.3.

(iii) draw requisite size of sample using SRS, equal, proportional and Neyman

allocation.

(iv) find estimates of population mean and population variance for each allocation.

(v) estimate the gain in efficiency due to stratification using proportional and

Neyman allocation.

2. Table 1 shows the stratification of some factories in the state of Maharashtra,

India, for the year 1981-82 by the industry group (according to the National

Industrial and Occupational Classification). For a sample of 500 factories

compute the sample sizes in each stratum under

(a) proportional allocation, and

(b) optimum allocation. Compare the precision of these estimates with that of the

mean per unit estimator under simple random sampling.

Table 1

_______________________________________________________________

Industry Number of Average number Standard deviation

Group factories of workers ( )hY ( )hs

_______________________________________________________________

331 327 92.1 200.78

343 139 58.7 140.29

345 203 19.5 36.66

354 170 49.5 94.54

360 177 142.2 372.56

367 89 45.8 53.59

3. Suppose that the population of size N (assuming that N = nk, n and k being integers)

into n strata where the stratum h contains units with labels

  nhkjjkhGn ,..,2,1,,..,2,1,)1( 

and one unit is selected from each stratum randomly to get a sample of size n. The

population values are modelled by the relation, NibiaYi ,..,1,  where a and b

are constants. Find the variance of the population total.

4. A sampler has two strata with relative sizes N

N W 1

1  and N

N W 2

2  . He believes

that 1S and 2S can be taken as equal. For a given cost 2211 nCnCC  , assuming

the each stratum size to be large, show that

2

211

2211

)2(

)(

WCW

CWCW

V

V

opt

prop



 

  



  

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