a) Describe an example of using stratified sampling. Explain the rationale for calling it stratified sampling and explain why stratified sampling is appropriate for this example.

b. Describe (a) an example of a population and (b) an example of a sample drawn from that population. What is the rationale for calling the selection a sample?

c. Describe one example each of (a) ordinal data, (b) interval data, and (c) ratio data. What is the rationale for the examples? I.e., what is it about them that makes each one suitable as an example of its data type?

Problem A

Below is an example of stratified sampling.

A researcher is studying the impact of self-esteem on academic achievement on undergraduate students that enroll in a psychology program at University X. To ensure that the study's sample is representative, the researcher randomly selects 100 freshmen, 100 juniors, 100 sophomores, and 100 seniors as participants. This sampling method can be considered as a stratified random sampling since the researcher randomly selects 100 participants from each subpopulation.

Problem B

Using the example provided by problem A, the population of the study is all undergraduate students that enroll in a psychology program at University X. The sample of the study is the 400 participants randomly selected from the student list. The 400 participants can be considered as a sample because they are individuals selected from the population.

Problem C

One example of ordinal data is academic ranks. Academic ranks can be considered as ordinal data because the data has quantitative value (e.g., the 10th rank is lower than the 8th rank) but the distance between each data is not fixed (e.g., the distance between the 1st rank and 2nd rank may not be the same as the distance between the 2nd rank and the 3rd rank).

One example of interval data is temperature. Temperature can be considered as interval data because the data has quantitative value (10 degrees Celsius is higher than 5 degrees Celsius), the distance between each data point is fixed (e.g., the distance between 5 degrees Celsius and 3 degrees Celcius is the same as the distance between 7 degrees Celcius and 5 degrees Celcius), but the data has no absolute zero (i.e., 0 degrees Celcius does not mean that there is no temperature).

One example of ratio data is bodyweight. Bodyweight can be considered as ratio data because the data has quantitative value (10 kgs is heavier than 5 kgs), the distance between each data point is fixed (e.g., the distance between 8 kgs and 5 kgs is the same as the distance between 24 kgs and 21 kgs), and the data has an absolute zero (i.e., 0 kilogram means that there is no bodyweight).