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Use probability proportional to size and systematic sampling to select 4 EBs fro

ID: 3357799 • Letter: U

Question

Use probability proportional to size and systematic sampling to select 4 EBs from 12 EBs below, and then select 30 households from each selected EB. Let 511 be the random start.

EB

Number of households

1

297

2

321

3

105

4

399

5

122

6

403

7

312

8

328

9

327

10

98

11

104

12

184

a)Select the four EBs.   

b)Find the first stage, second stage and overall probability for selecting households for each of the selected EB.   

c)If the mean values corresponding to the selected EBs (in that order) are 4.5., 3.7, 2.8 and 3.3, find Upps  and place a bound on the error of estimation (B).

EB

Number of households

1

297

2

321

3

105

4

399

5

122

6

403

7

312

8

328

9

327

10

98

11

104

12

184

Explanation / Answer

Probability of Selection of EB

EB

Number of House Holds

c.f.

Probability

Y

X

1

297

297

0.099

2

321

618

0.107

3

105

723

0.035

4

399

1122

0.133

5

122

1244

0.040666667

6

403

1647

0.134333333

7

312

1959

0.104

8

328

2287

0.109333333

9

327

2614

0.109

10

98

2712

0.032666667

11

104

2816

0.034666667

12

184

3000

0.061333333

Total

3000

1

(a) Selection of sample of size 4 (i.e. Selection of four EB's by Simple Random Sampling without Replaement)

Note that, the random number generated in excel worksheet using commad [=randbetween(1,3000)]

Random Number

Selected Unit in the sample

first unit (EB) of the sample

210

1

second unit (EB) of the sample

1490

6

third unit (EB) of the sample

918

4

fourth unit (EB) of the sample

2871

12

(b) Selection of 30 house holds by sysetematic sampling (Second Stage)

the polpulation for second stage sample

1

297

4

399

6

403

12

184

Total

1283 (N)

The population size N= 1283

Sample size n= 30

sampling interval k=N/n 42.76666667 = 43(approx)

Random start i= 511 (given)

The house hold selected in the Sample are given as below

Serial Number

Sample House holds

1

511

2

554

3

597

4

640

5

683

6

726

7

769

8

812

9

855

10

898

11

941

12

984

13

1027

14

1070

15

1113

16

1156

17

1199

18

1242

19

2

20

45

21

88

22

131

23

174

24

217

25

260

26

303

27

346

28

389

29

432

30

475

EB

Number of House Holds

c.f.

Probability

Y

X

1

297

297

0.099

2

321

618

0.107

3

105

723

0.035

4

399

1122

0.133

5

122

1244

0.040666667

6

403

1647

0.134333333

7

312

1959

0.104

8

328

2287

0.109333333

9

327

2614

0.109

10

98

2712

0.032666667

11

104

2816

0.034666667

12

184

3000

0.061333333

Total

3000

1