Question

Describe how to obtain a sample of eight people in that classroom so that the result is a sample of the given type. (You should have two answers, one for each type)

a. Systematic sample

b. Stratified sample

..real stuck will give you great feedback and thumbs up

Answer 1

Systematic sampling:  Suppose that the N units in the population are numbered 1 to N in some order. Suppose N=nk where n is the sample size and k is an integer. A number is taken at random from the number 1 to k using random number table. Suppose random number is i is obtaineed. Then the systametic sample will contain n units with serial number {i, i+k, i+2k,.....,(n-1)k}.
Thus the sample consist of the first unit selected at random and every k^th unit thereafter.

Suppose we have population of size N=24 with population units {X₁, X₂, .......,X₂₄}
Sample size n=8
Therefore k=3
Let random number selected is 2
Then the sample units are {X₂, X₅, X₈, X₁₁, X₁₄, X₁₇, X₂₀, X₂₃}

Stratified Sampling: In stratified sampling the population of N units is first divided into subpopulation of N₁, N₂,.....N_L units. These sub population is non-overlapping and together they comprise the whole population. When the strata have been determined sample is drawn from each strata. Say n₁, n₂,......n_L be the sample size drawn from i th strata respectively and together they comprise the desired sample size that is n₁+n₂+....+n_L=n

Again let we have population of size N=24 with population units {X₁, X₂, .......,X₂₄}
Sample size n=8
Let us devide the population in 3 stratas
Say,

Let us take 2 , 3 , 3 samples from the strata respectively. we select sample units ramdomly within strata
Suppose we get {X₂ , X₇} from strata 1 , {X₁₁, X₁₂,X₁₄} from strata 2 and {X₁₇, X₂₃, X₂₄} from strata 3
Then our sample of size 8 is {X₂ , X₇, X₁₁, X₁₂,X₁₄, X₁₇, X₂₃, X₂₄}