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(solution) Microsoft Word - Assignment 4.docx 1. Suppose you identified

Microsoft Word - Assignment 4.docx

1. Suppose you identified schools as clusters and randomly picked FAU and Duke out of all four schools. Which students would be included in the sample, if you were to follow cluster sampling? Use the random numbers 0.82, 0.78, 0.66, and 0.47. List the student names and briefly explain your answer.

2. Suppose you identified schools as clusters and randomly picked FAU and Duke out of all four schools. Which students would be included in a sample of 8 (4 from each school), if you were to follow multi-stage sampling? Use the random numbers 0.44, 0.35, 0.91, and 0.97 for FAU and 0.12, 0.59, 0.70, and 0.27 for Duke. List the student names, show your work, and briefly explain your answer.

3. Assume that you are marketing GMAT services and only students who are interested in applying for graduate school are likely to buy these kind of services. Suppose you decided to follow purposive sampling and target only those students with a GPA of 3.0 or higher in all four schools. Which students would be included in a sample of 4? Use the random numbers 0.17, 0.26, 0.37, and 0.90. List the student names, show your work, and briefly explain your answer.

4. Assume this time you want to break the students with a GPA of 3.0 or higher (in all schools) into two groups: first group with GPA 3.0-3.5 and second group with GPA 3.6-4.0. Suppose you decided to follow quota sampling by picking 2 students from each group and form a sample of 4 students. Which students would be included this sample? Use the random numbers 0.88 and 0.72 for the first group (GPA 3.0-3.5) and 0.73 and 0.15 for the second group (GPA 3.6-4.0). List the student names, show your work, and briefly explain your answer.

CHAPTER 5: SAMPLING EXAMPLES

Sequence Name Gender (female=1, male=0) School GPA 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40 Adam

Alexandra

Beth

Bryan

Carol

Cindy

Deanna

Donald

Elizabeth

Eric

Francine

Frank

George

Greg

Holly

Ileana

Isabelle

Jose

Karyn

Kyle

Lamar

Latrell

Leslie

Max

Melissa

Michael

Molly

Nancy

Norman

Otto

Patricia

Paul

Ricardo

Sally

Simon

Suzanne

Tara

Tim

Todd

Yanissa 0

1

1

0

1

1

1

0

1

0

1

0

0

0

1

1

1

0

1

0

0

0

1

0

1

0

1

1

0

0

1

0

0

1

0

1

1

0

0

1 Stanford

Stanford

Cornell

FAU

Stanford

Stanford

Duke

Cornell

FAU

Duke

Duke

FAU

Stanford

Stanford

Duke

FAU

Cornell

Cornell

Duke

FAU

Stanford

Stanford

FAU

Stanford

Cornell

FAU

Duke

FAU

Stanford

Duke

FAU

FAU

Cornell

Duke

Duke

Stanford

Stanford

Cornell

Cornell

FAU 3.0

1.4

1.2

2.7

2.8

3.5

3.4

3.6

2.0

2.3

4.0

4.0

3.8

3.3

2.8

0.2

2.3

3.0

3.1

3.2

3.3

2.7

3.3

2.4

3.6

3.0

2.9

3.0

2.9

1.8

3.5

2.5

2.3

3.0

2.6

2.6

3.7

2.4

2.0

2.0 Table of random numbers:

0.82 0.78 0.66 0.88 0.67 0.55 0.42 0.75 Sequence

for the male

strata

1 Sequence for

the female

strata

1

2 2

3

4

5

3

6

4

7

5

6

7

8

9

10

8

11

9

10

11

12

12

13

13

14

15

14

15

16

16

17

17

18

18

19

19

20 0.22 Notice: each time we use a new random number from the random number table! 20 SIMPLE RANDOM: Pick a sample of 4 people from the list.

[sequence # to pick] = [random #] × [total #of subjects]

1st record to pick

2nd record to pick

3rd record to pick

4th record to pick = .82 × 40 = 32.80 ? 33

= .78 × 40 = 31.20 ? 31

= .66 × 40 = 26.40 ? 26

= .88 × 40 = 35.20 ? 35 Ricardo

Patricia

Michael

Simon SYSTEMATIC: Pick a sample of 4 people from the list.

[interval length] = [population] / [sample size]

Interval length = 40/4 = 10

[initial record picked] = [interval length] × [random #]

Initial record picked = 10 × .67 = 6.70 ? 7

Deanna

[next record to pick] = [previous pick] + [interval length]

2nd record to pick

= 6.70 + 10 = 16.70 ? 17 Isabelle

3rd record to pick

= 16.70 + 10 = 26.70 ? 27

Molly

4th record to pick

= 26.70 + 10 = 36.70 ? 37

Tara STRATIFIED RANDOM:

Simple random sampling yielded 3 males & 1 female and systematic sampling yielded 4 females, but

we?d like the proportion of each gender in our sample to resemble those in the target population.

[number to select from strata]

= [sample size] × {[strata size]/[population]}

# females needed = 4 × {20/40} = 2

# males needed = 4 ? 2 = 2

Next, divide the population into two strata: males versus females.

Re-sort students by alphabetical order within each strata (see the last two columns in the table above).

Finally, pick two from each group using simple random sampling.

Males:

1st record to pick

2nd record to pick = .55 × 20 = 11.00 ? 11

= .42 × 20 = 8.40 ? 8 Latrell

Jose Females:

1st record to pick

2nd record to pick = .75 × 20 = 15.00 ? 15

= .22 × 20 = 4.40 ? 4 Nancy

Cindy

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