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Chapter 3: Problem 4

Identify the sampling method. Just the name will suffice. a. Researchers select every 5 th customer who walks into the store to take a survey. b. Raffle tickets are distributed and collected in a bag, where they are mixed and ten are drawn for prizes. c. I asked the shoppers near me in the shoe department what size they wear. d. An IRS auditor randomly selects 25 taxpayers in each filing status (single, head of household, married filing jointly, and married filing separately).

Short Answer

Expert verified
a) Systematic sampling b) Simple random sampling c) Convenience sampling d) Stratified sampling

Step by step solution

01

Understanding the Selection Method for Part (a)

In this scenario, researchers use a systematic method by choosing every 5th customer. This is systematic sampling as it selects participants at regular intervals.
02

Analyzing the Selection Process for Part (b)

Here, raffle tickets are distributed, mixed thoroughly, and then drawn randomly. This describes a simple random sampling method since every ticket has an equal chance of being chosen.
03

Examining the Selection Strategy for Part (c)

The shoppers near me are being asked about their shoe size. This is an example of convenience sampling, as it involves selecting individuals who are easiest to reach.
04

Evaluating the Selection Criteria for Part (d)

The IRS auditor selects a specific number of individuals from different filing statuses. This approach uses stratified sampling, as the population is divided into subgroups and random samples are taken from each group.

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Key Concepts

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

Systematic Sampling
Systematic Sampling is a straightforward method where researchers select subjects at a regular interval. Imagine you're in a store and you decide to survey every 5th person that enters. This way, you create a simple pattern in selecting your sample, ensuring a fair representation over time.
There are a few benefits to this method:
  • It's easy and quick once you determine the starting point and interval.
  • It provides a simple way to spread your sample evenly across the population.
However, ensure there's no hidden pattern within the population that could skew your results. For example, if every 5th customer always happens to be elderly, your sample might not be as random as you intended.
Simple Random Sampling
Simple Random Sampling is like drawing names from a hat! In this method, every individual in your population has an equal chance of being selected for your sample. Imagine a raffle where every ticket has an equal chance of being picked. By mixing all your tickets thoroughly, you ensure true randomness.
The key advantages of simple random sampling include:
  • It gives each subject an equal chance, promoting fairness.
  • It's straightforward and easy to understand.
However, it can be tricky if your population is very large or difficult to list all members. Also, sometimes it's not the most efficient method if certain subgroups are missed entirely just by chance.
Convenience Sampling
Convenience Sampling is all about ease. This method entails selecting participants that are most accessible to the researcher. For instance, if you're curious about shoe sizes and ask customers standing near you in a shoe store, you're employing convenience sampling.
Though exceptionally efficient and easy, this method has its drawbacks:
  • It lacks randomness and therefore can lead to bias.
  • Results might not be representative of the broader population.
Despite these cons, convenience sampling can be useful for preliminary research or when resources are limited.
Stratified Sampling
Stratified Sampling is a more refined approach. It involves dividing your population into distinct subgroups and then sampling from each subgroup. Imagine an IRS auditor choosing a specific number of taxpayers from each filing status category. This ensures representation across various segments.
The primary benefits of stratified sampling include:
  • It can increase precision and accuracy by acknowledging different subgroups.
  • Facilitates a proportional representation which might be vital in certain studies.
Nevertheless, it requires a good understanding of your population's structure and might involve more extensive planning than some simpler methods.

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