Question

Consider that I have 4 sections of Stat 200. Section 001 has 40 students, section 002 has 40 students, section 003 has 30 students and section 004 has 40 for a total of 150 students. I'd like to do a satisfaction survey with a sample size of 30, but I suspect that the section may change students' satisfaction with the course.

a. Which sampling techniques could I use to ensure I get a representative sample from each section? (Check the two best answers!)

• Systematic Sampling
• Cluster Sampling
• Simple Random Sampling
• Stratified Sampling

b.Please first set your random seed to 4500 if you have a Ti 83/84 Calculator (type 4500, STO - Math - PRB - enter twice). Now, assigning numbers 1 through 150 to the students and using one of your sampling techniques above (state which one you choose) and your random sample application on your calculator, find 30 numbers associated with the students who will be chosen.

Answer 1

Que.a Stratified sampling

In stratified sampling, the researcher divides the population into separate groups, called strata. Then, a probability sample (often a simple random sample ) is drawn from each group.

Que.b

Our strata's have sample size 40, 40 , 30 and 40. Now we find the sample size drawn from each strata.

For strata with size 40 :

For strata with size 30 :

So we draw simple random sample of size 8 from first, second and fourth strata and simple random sample of size 6 is drawn from third strata.

Step.1 4500 --> STO ---> Math ---> PRB ---> Enter twice

Step.2 Math ---> PRB --> Enter ---> randIntNoRep(1,40)

Step.3 4500 --> STO ---> Math ---> PRB ---> Enter twice

Step.4 Math ---> PRB --> Enter ---> randIntNoRep(41,80)

Step.5 4500 --> STO ---> Math ---> PRB ---> Enter twice

Step.6 Math ---> PRB --> Enter ---> randIntNoRep(81,110)

Step.7 4500 --> STO ---> Math ---> PRB ---> Enter twice

Step.8 Math ---> PRB --> Enter ---> randIntNoRep(111,150)

From first strata we get 32,31,30, 20,12,35,18,38, 27

From second strata: 72, 71 ,70, 60, 52, 75, 58, 78

From third strata : 96, 102, 89, 88, 103, 109, 83

From fourth strata : 142, 141, 140, 130, 122, 145, 128, 148