Question

In: Statistics and Probability

The following is a list of the first names of 24 fictional students in a statistics...

The following is a list of the first names of 24 fictional students in a statistics class at Cleveland State University. The students are identified by numbering them 01 through 24.
A sample of six students is to be selected by using systematic sampling. The first student to be selected is the one with ID 03. Choose the six students that will be included in the sample.

ID Student ID Student
01 Ali 13 Sakiya
02 Pedro 14 Mary
03 Alicia 15 Ethan
04 Jalil 16 Nathan
05 Tonika 17 Patricia
06 Charles 18 Chung
07 Everlyn 19 Sally
08 Saul 20 Clarence
09 Sarah 21 Susie
10 Leroy 22 Mohammed
11 Joan 23 Maria
12 Raul 24 Sajida

Solutions

Expert Solution

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.

here population size = 24

desired sample size = 6

for interval calculation,

interval = 24 / 6 = 4

random starting point is 3 and from interval we can easily obtain six students that will be included in the sample.

3+4 = 7

7+4 = 11

11+4 =15

15+4 = 19

19+4 = 23

hence six students that will be included in the sample who have ID 3,7,11,15,19,23

ID Student ID Student
01 Ali 13 Sakiya
02 Pedro 14 Mary
03 Alicia 15 Ethan
04 Jalil 16 Nathan
05 Tonika 17 Patricia
06 Charles 18 Chung
07 Everlyn 19 Sally
08 Saul 20 Clarence
09 Sarah 21 Susie
10 Leroy 22 Mohammed
11 Joan 23 Maria
12 Raul 24 Sajida
03 Alicia
07 Everlyn
11 Joan
15 Ethan
19 Sally
23 Maria

these are six students that will be included in the sample.


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