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

Identify Sampling Method For Situation A

In the first example, whole sections of a seminar course are being chosen at random and then all students in these sections are being selected. This is an example of cluster sampling because complete groupings (clusters) are selected.

02

Identify Sampling Method For Situation B

In the second situation, researchers pick a specific number of faculty members, students, and staff each independently, at random. This kind of selective sampling process from different groups (or strata) indicates stratified random sampling.

03

Identify Sampling Method For Situation C

In this scenario, the researcher has selected the students of a specific class he teaches, because they're conveniently accessible to him. This reflects a convenience sampling.

04

Identify Sampling Method For Situation D

Here, each senior has an equal chance to get selected. Names of all seniors are written on slips, mixed in a box, and then some slips are randomly picked. As every individual senior has an equal chance of being selected, this indicates simple random sampling.

05

Identify Sampling Method For Situation E

In this instance, every 50th person after the 24th attendee is selected. This patterned way of selecting participants suggests systematic sampling.

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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 you select entire groups rather than individual members. Imagine a school with 30 sections of a seminar course and you need to study freshmen. Instead of picking individual students, you randomly pick 4 sections and include every student in these sections in your sample.

This approach can save time and resources when dealing with a large population.

• Pros: Efficient and practical for large groups.
• Cons: May not reflect the entire population very accurately if clusters are not homogeneous.

It’s like choosing a full basket of apples to examine to get an idea of their overall quality rather than sampling individual apples at random.

Stratified Random Sampling

Stratified random sampling involves dividing a population into distinct subgroups, or 'strata', and randomly selecting members from each stratum. Consider a university where you want a sample of students, faculty, and staff. You first divide them into these groups and randomly select a set number from each group, such as 50 faculty members, 100 students, and 30 staff.

The purpose is to ensure that the sample accurately reflects the population’s diversity.

• Pros: Increases precision and represents all subgroups.
• Cons: Requires clear stratification criteria which can sometimes be hard to define.

This method is like ensuring you taste all sections of a layered cake to get a full sense of its flavor.

Convenience Sampling

Convenience sampling involves selecting a sample that is easy to access. Imagine a professor using the students from his own class because they are right there and easy to include.

• Pros: Simple and quick to implement.
• Cons: Risk of bias as the sample may not represent the broader population.

It’s similar to picking fruits from the front row at the market because they’re within reach, not necessarily because they best represent the batch.

Simple Random Sampling

Simple random sampling ensures each member of a population has an equal chance of being selected. Picture writing every high school senior's name on slips of paper, mixing them in a box, and drawing picks randomly. This method is often seen as the gold standard in sampling for its fairness and simplicity.

• Pros: Minimizes bias and easy to understand.
• Cons: Can be impractical with very large populations due to difficulty in listing everything.

Think of it as drawing names out of a hat—straightforward and free from favoritism or patterns.

Systematic Sampling

Systematic sampling involves selecting every 'k-th' member from a list. For instance, every 50th person entering a venue after starting with the 24th is chosen. This method creates a regular sampling interval, resulting in a structured selection process.

• Pros: Methodical and simple to execute without a need for a complete population list.
• Cons: Risks introducing bias if there is a hidden order in the way the population is listed.

This is akin to picking every nth item off a conveyor belt, ensuring a consistent spread across the sample.