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 freshmen 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 4 sections of the seminar course at random from the 30 sections and all students in the 4 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

Identifying Sampling Method used in Scenario A

In scenario A, all the freshmen at a university are divided into 30 sections and out of these, 4 sections are selected at random and every student in these sections is included in the sample. This is a clear example of cluster sampling, where a group or 'cluster' is chosen at random and everyone in that group is sampled.

02

Identifying Sampling Method used in Scenario B

In scenario B, a researcher randomly selects 50 faculty members, 100 students and 30 staff members all separately from their own lists. Here, each group is treated as a 'stratum' and a random sample is gathered from each stratum. Therefore, the sampling method used here is a stratified random sampling.

03

Identifying Sampling Method used in Scenario C

In scenario C, a researcher uses all 85 students enrolled in his Psychology 101 class to conduct his research, this is most likely due to convenience, therefore, this is a case of convenience sampling algorithm.

04

Identifying Sampling Method used in Scenario D

In scenario D, a researcher selects 10 students randomly from all seniors by using slips of paper and a box. This is an example of simple random sampling, where each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample.

05

Identifying Sampling Method used in Scenario E

In scenario E, a researcher selects the 24th person entering through the door and then every 50th person thereafter. This is an example of systematic sampling which relies on arranging the target population according to some ordering scheme and then selecting elements at regular intervals through that ordered list.

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Key Concepts

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

Cluster Sampling

Cluster Sampling is a method where the population is divided into groups, known as clusters. These clusters are often naturally occurring groups within the population, for example, classes in a school.
Instead of sampling individuals directly, entire clusters are selected at random. Once a cluster is chosen, all members within that cluster are included in the sample.
This method is particularly useful when dealing with large populations that are geographically spread out.

• Efficient: Reduces travel and logistical effort when assessing widespread populations.
• Cost-effective: More economic than sampling individuals separately.
• Risk of bias: If clusters are homogenous, the sample may not reflect population diversity.

To apply cluster sampling effectively, make sure your clusters are representative of the entire population. This will help maintain the integrity of your research results.

Stratified Random Sampling

Stratified Random Sampling involves dividing a population into subgroups known as strata. These strata are based on shared characteristics, such as age, gender, or income level.
Within each stratum, random samples are taken to ensure that the sample reflects the diversity of the whole population.

• Increased accuracy: Provides detailed and precise representation of diverse populations.
• Control over subgroups: Ensures each subgroup is represented in the sample.
• Time consuming: Requires detailed knowledge about the population to create accurate strata.

It's important to clearly define your strata to avoid overlap. Advantageously, this method helps in comparing different subgroups within a population.

Convenience Sampling

Convenience Sampling is a non-probability method where samples are taken from a group that is easy to access or nearby to the researcher. This often means using readily available participants.
While convenient and quick, this method may not accurately represent the broader population.

• Quick and easy: Saves time with fast data collection.
• Cost-Effective: Requires fewer resources.
• Bias risk: High potential for sampling bias, limiting generalizability.

This method is best used when time and resources are limited, or when generalization to the whole population is not necessary.

Simple Random Sampling

Simple Random Sampling ensures each member of the population has an equal chance of being chosen. This is achieved through random selection, often using tools like random number generators.
It's a straightforward approach that avoids bias by ensuring all individuals have the same probability of selection.

• Unbiased: Every member has an equal opportunity to be selected.
• Simplicity: Easy to understand and implement.
• Limited practical utility: Challenging with large populations due to logistical constraints.

To maximize effectiveness, ensure your selection process remains truly random and covers the whole target population.

Systematic Sampling

Systematic Sampling involves selecting elements from an ordered list at regular intervals. This method is useful for populations already organized in some way, such as numbered lists.
After choosing a random starting point, say the 24th person, every nth member from that point is selected until the sample size is reached.

• Simple strategy: Easy to implement once a list is established.
• Efficient: Reduces randomness, simplifying sampling process.
• Risk of hidden patterns: Ensure no hidden trends within the list that could skew findings.

This method is excellent for certain structured populations but should be applied with caution to avoid periodicity issues.