Question

(1 point) For each problem, select the best response.

(a) A simple random sample of size n is defined to be

A. a sample of size n chosen in such a way that every unit in the population has the same chance of being selected.
B. a sample of size n chosen in such a way that every set of n units in the population has an equal chance to be the sample actually selected.
C. a sample of size n chosen in such a way that every unit in the population has a known nonzero chance of being selected.
D. All of the above. They are essentially identical definitions.

(b) In order to take a sample of 1200 people from a population, I first divide the population into men and women, and then take a simple random sample of 500 men and a separate simple random sample of 700 women. This is an example of a

A. a simple random sample.
B. convenience sampling.
C. stratified random sample.
D. a multistage sample.
E. randomized comparative experiment.

(c) A small college has 500 male and 600 female undergraduates. A simple random sample of 50 of the male undergraduates is selected, and, separately, a simple random sample of 60 of the female undergraduates is selected. The two samples are combined to give an overall sample of 110 students. The overall sample is

A. convenience sampling.
B. a systematic sample.
C. a multistage sample.
D. a stratified random sample.
E. a simple random sample.

Answer 1

Simple Random Sampling: A simple random sample (SRS) of size n is produced by a scheme which ensures that each subgroup of the population of size n has an equal probability of being chosen as the sample.

Stratified Random Sampling: Divide the population into "strata". There can be any number of these. Then choose a simple random sample from each stratum. Combine those into the overall sample. That is a stratified random sample. (Example: Church A has 600 women and 400 women as members. One way to get a stratified random sample of size 30 is to take a SRS of 18 women from the 600 women and another SRS of 12 men from the 400 men.)

Multi-Stage Sampling: Sometimes the population is too large and scattered for it to be practical to make a list of the entire population from which to draw a SRS. For instance, when the a polling organization samples US voters, they do not do a SRS. Since voter lists are compiled by counties, they might first do a sample of the counties and then sample within the selected counties. This illustrates two stages. In some instances, they might use even more stages. At each stage, they might do a stratified random sample on sex, race, income level, or any other useful variable on which they could get information before sampling.

Systematic sampling: Individuals are selected at regular intervals from the sampling frame. The intervals are chosen to ensure an adequate sample size.

convenience sampling: It is a type of non-probability sampling method where the sample is taken from a group of people easy to contact or to reach. For example, standing at a mall or a grocery store and asking people to answer questions would be an example of a convenience sample.There are no other criteria to the sampling method except that people be available and willing to participate.

ANSWERS:

a) A simple random sample of size n is defined to be- D.All of the above. They are essentially identical definitions.( as all the three options i.e, A,B,C says that every unit in the population has the same chance of being selected.)

b) In order to take a sample of 1200 people from a population, I first divide the population into men and women, and then take a simple random sample of 500 men and a separate simple random sample of 700 women. This is an example of a- C. stratified random sample.( as here we divide the population into two strata i.e, male and female and then take samples by SRS)

(c) A small college has 500 male and 600 female undergraduates. A simple random sample of 50 of the male undergraduates is selected, and, separately, a simple random sample of 60 of the female undergraduates is selected. The two samples are combined to give an overall sample of 110 students. The overall sample is- D. a stratified random sample.( as here also we divide the population into two starta)

NOTE- Don't confuse stratified random sampling with multistage random sampling.

Stratified is taking random samples from sections of the population, say NJ, CA, and FL so that those 3 states are represented in the sample.

Multistage means randomly selecting clusters in the population, then SRSing clusters in those clusters, etc, etc.