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

(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