91Ó°ÊÓ

For each of the situations described, state whether the sampling procedure is simple random sampling, stratified random sampling, cluster sampling, systematic sampling, or convenience sampling. a. All first-year students at a university are enrolled in 1 of 30 sections of a seminar course. To select a sample of freshmen at this university, a researcher selects four sections of the seminar course at random from the 30 sections and all students in the four selected sections are included in the sample. b. To obtain a sample of students, faculty, and staff at a university, a researcher randomly selects 50 faculty members from a list of faculty, 100 students from a list of students, and 30 staff members from a list of staff. c. A university researcher obtains a sample of students at his university by using the 85 students enrolled in his Psychology 101 class. d. To obtain a sample of the seniors at a particular high school, a researcher writes the name of each senior on a slip of paper, places the slips in a box and mixes them, and then selects 10 slips. The students whose names are on the selected slips of paper are included in the sample. e. To obtain a sample of those attending a basketball game, a researcher selects the 24 th person through the door. Then, every 50 th person after that is also included in the sample.

Step by step solution

01

Identify Sampling Procedure in Situation a

In situation a, randomly selected groups (sections) are chosen where everyone within these groups is included in the sample. This type of sampling is known as cluster sampling.

02

Identify Sampling Procedure in Situation b

In situation b, the sample is randomly selected from different groups (students, faculty, and staff) it's known as stratified random sampling. This is because the researcher independently samples from within each mutually exclusive group(stratum).

03

Identify Sampling Procedure in Situation c

In situation c, the researcher conveniently picks the students in his course for his research sample without any random selection from the entire university students, which is characteristic of convenience sampling.

04

Identify Sampling Procedure in Situation d

In situation d, the researcher uses a process where each individual of the population has an equal opportunity of being picked. This is the main characteristic of simple random sampling.

05

Identify Sampling Procedure in Situation e

In situation e, the sampling is conducted at regular intervals (50th individual after the 24th one). This kind of sampling where sampling is made at regular intervals is known as systematic sampling.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simple Random Sampling

Simple random sampling is a method where every member of a population has an equal chance of being selected. Think about it as a lottery system where each participant's number could be drawn from a hat.

For example, when selecting a group of seniors from a high school for a study, if a researcher writes each name on a slip of paper and draws some names without looking, this ensures no bias in the selection process. Everyone has the same chance to be picked, and this method reflects the actual diversity of the whole senior class.

This method is straightforward but it’s essential that the sample is completely randomized to avoid any form of bias, thus making the results of the study truly representative of the entire population.

Stratified Random Sampling

Stratified random sampling involves dividing the population into smaller groups, known as strata, that share a similar characteristic, like age or occupation. Then, a random sample from each stratum is taken proportional to the stratum's size relative to the population.

Consider a university wanting to understand its community's opinions. They could divide their population into three strata: faculty, students, and staff. They would then select a random sample from each stratum to ensure they are represented in their study according to their presence in the total university population.

This technique is particularly useful when there are distinct sub-groups within a population, and we want to guarantee each group's representation in the sample. It reduces sampling error compared to simple random sampling and improves the accuracy of the results for the subgroups.

Cluster Sampling

Cluster sampling differs from stratified sampling in that it selects all members from randomly chosen groups or clusters rather than from stratified layers of the population. Imagine slicing a cake into even pieces (clusters) and then picking a few pieces randomly and using all the cake in those selected pieces (clusters).

In the context of surveying first-year university students, if sections of a seminar course represent these clusters, a researcher may randomly choose a few sections and include all the students from those sections in the study.

This approach can be cost-effective and time-efficient, especially when dealing with a large, widely dispersed population. However, the catch is that the clusters need to be as representative as possible of the population to avoid bias.

Systematic Sampling

Systematic sampling is when you select members of a population at regular intervals. This method might be likened to skipping stones across a pond; you pick every 'kth' stone (or person) to be in your sample.

An example would be selecting every 50th person who enters a stadium for a game. You'd start at a random point (like the 24th person) and then select every 50th person after that. The start point should be chosen randomly to maintain the randomness of the sampling method.

This sampling method may be easier to implement than simple random sampling and is useful when dealing with a large population. However, it assumes that the population is ordered randomly, as patterns in the data could lead to biased results if the interval aligns with the pattern.

Convenience Sampling

Convenience sampling refers to choosing members of a population that are easy to reach or 'convenient' for the researcher. This method often involves taking a sample from a group that is readily available rather than randomly.

For instance, a university researcher may use students from a class they are teaching as the sample for their study. While this is certainly an easy way to gather participants, it does not offer the benefits of randomization found in other methods and is, therefore, likely to introduce bias into the results. The sample might not accurately represent the larger population because it is based on availability, not randomization.

This method is generally not advised for rigorous research studies where representing the larger population is essential. It’s more commonly used in exploratory research, where generating quick and easy insights is the primary goal rather than establishing a broad generalization.