Question

In Exercises 9–12, identify the type of sample and explain why the sample is biased. You want to find out whether booth holders at a convention were pleased with their booth locations. You divide the convention center into six sections and survey every booth holder in the fifth section.

Short answer

The type of sample is a Cluster Sample and it's biased because it only includes data from the fifth section of the convention center, ignoring potential variations and perspectives of booth holders in other sections

Step-by-step solution

Identifying the type of sample

The type of sample represented here is a Cluster Sample. In a cluster sample, the entire population is divided into groups, or clusters, and a random selection of these clusters are chosen. All observations from the chosen clusters are included in the sample. Here, the entire population of booth holders is divided into six segments or 'clusters', and only one segment - the fifth one - is surveyed.

Discussing Bias

Biased sampling is when some elements of the population are systematically more likely to be chosen in a sample than others. In this particular case, the chosen sample only represents booth holders from the fifth section, and hence does not represent the entire population of booth holders at the convention. Opinions of booth holders from the other five sections are not considered in this survey. Hence, this makes the sampling biased, as people in different sections may have different perspectives on their booth locations depending on various factors like proximity to entrance/exit, visibility, footfall, etc.

Key concepts

Cluster Sampling

Cluster sampling is a method used when you want to gather data from a large population but aim to reduce costs and increase efficiency. It involves dividing the population into segments, known as clusters. Instead of sampling randomly from the entire population, you select entire clusters to represent the whole group.
In the example exercise, the convention center is divided into six different sections, each acting as a separate cluster. The survey was conducted only in the fifth section, making it an example of cluster sampling. Each booth holder in that section was surveyed, which helps to ease data collection. However, it's important to note that not choosing clusters at random might lead to bias if the chosen cluster doesn't represent other clusters well. It is crucial to ensure that clusters are representative to avoid skewed results.

Survey Methodology

Survey methodology is a field that focuses on the development and implementation of surveys. It ensures accurate data collection and reliable results.
There are several important aspects of survey methodology:

• Design: Careful planning to determine how to collect data accurately.
• Sampling Method: Deciding whether to use a method like cluster sampling.
• Question Phrasing: Questions should be clear and unbiased to gather genuine responses.

In the context of the exercise, the chosen survey method was cluster sampling. Although it's efficient, it's critical to ensure that it does not limit the survey's accuracy by introducing bias, impacting the interpretation of booth holders' satisfaction.

Sample Representativeness

Sample representativeness refers to how well a sample reflects the population from which it is drawn. Ideally, a representative sample captures the diversity within the entire population.
In our exercise, only one section (or cluster) was surveyed. To achieve representativeness, it's important to ensure that the chosen cluster mirrors the characteristics of the entire population of booth holders. For example, booth holders in the selected cluster should ideally have similar location experiences to those in other sections. However, if the section near exits or entrances is chosen, it might not reflect the experiences of those placed in less significant spots, leading to a non-representative sample.

Population Bias

Population bias occurs when the selected sample over-represents certain elements of the population, skewing the results. This bias can mislead researchers into drawing inaccurate conclusions about the entire population.
In the case given, only the fifth cluster of booth holders was surveyed, leaving out opinions from the other five sections. Potential differences in experiences, influenced by factors such as location within the convention center, can lead to biased results. For instance, booths in busier areas might report higher satisfaction simply due to increased foot traffic. Understanding and mitigating population bias is crucial in conducting objective and reliable surveys.