Question

1. your school has a pep rally in the gymnasium. the following is a map of the gym, where each box represents a seat that a student sits in.

freshman: seats 1 - 150
sophomores: seats 151 - 300
juniors: seats 301 - 450
seniors: seats 451 - 600
describe how you would use a random number generator to select 40 students to complete a survey with each of the following sampling methods. *note: i want you to describe it, not actually do it!
(a) simple random sample
(b) stratified random sample
(c) cluster sample

Explanation:

(a) For a simple random sample, assign each of the 600 seats a unique number from 1 - 600. Use the random - number generator to generate 40 distinct numbers within the range of 1 - 600. The students sitting in the seats corresponding to these numbers will be selected for the survey.
(b) For a stratified random sample, first note that there are 150 freshmen (seats 1 - 150), 150 sophomores (seats 151 - 300), 150 juniors (seats 301 - 450), and 150 seniors (seats 451 - 600). Calculate the proportion of students to be selected from each class. Since we want 40 students in total, we select $\frac{40}{4}=10$ students from each class. For freshmen, use the random - number generator to generate 10 distinct numbers in the range 1 - 150. For sophomores, generate 10 distinct numbers in the range 151 - 300. For juniors, generate 10 distinct numbers in the range 301 - 450. For seniors, generate 10 distinct numbers in the range 451 - 600. The students sitting in the seats corresponding to these generated numbers will be selected.
(c) For a cluster sample, divide the gym into, say, 10 clusters (for example, groups of 60 consecutive seats). Use the random - number generator to select 4 clusters. All the students sitting in the seats within the selected 4 clusters will be included in the survey.

Answer:

(a) Assign numbers 1 - 600 to seats. Generate 40 distinct random numbers in 1 - 600. Select students in corresponding seats.
(b) Calculate 10 students per class. Generate 10 distinct random numbers for each class's seat range. Select students in corresponding seats.
(c) Divide gym into clusters. Select 4 clusters with random - number generator. Include all students in selected clusters.