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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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