Question

In Exercises 9–12, identify the type of sample and explain why the sample is biased. Every tenth employee who arrives at a company health fair answers a survey that asks for opinions about new health-related programs.

Short answer

The type of sampling used is systematic sampling. The bias originates from only surveying every tenth employee who arrives at the health fair. This could potentially lead to the sample not being representative of all employee opinions, especially those who arrived later or did not attend the event.

Step-by-step solution

Identify the Type of Sampling

Here, every tenth employee who arrives at a company health fair is asked to take the survey. This method is a form of systematic sampling, since the selection of the sample members follows a specific, systematic order.

Identify the Bias Source

The sample could potentially be biased since it only includes every tenth employee who arrives at the health fair. This might overlook a broad range of opinions, especially those from employees who could not make it to the health fair in time or at all.

Explain the Consequences of the Bias

The bias in this sampling process might lead to results that do not accurately represent the whole population's opinions, because the sample only represents a very specific portion of employees, i.e., those who show up early at the health fair.

Key concepts

Systematic Sampling

Systematic sampling is a statistical method where members are selected from a larger population according to a fixed, periodic interval. For instance, in the provided exercise, every tenth employee who arrives at a health fair is chosen to participate in a survey. This method is often regarded as an intermediary between random sampling and convenience sampling.

While systematic sampling can be more straightforward to implement than purely random sampling, it may not always result in a representative sample, which is crucial for obtaining valid results. An important thing to remember is that this method assumes the population does not have an underlying order that could influence the trait being measured. In the exercise example, if certain types of employees arrive at the fair at similar times, the every-tenth-person rule could introduce bias.

Sampling Bias

Sampling bias occurs when a sample is collected in such a way that not all individuals, or some groups within the population, have an equal chance of being selected. This results in a sample that does not accurately reflect the makeup of the entire population, which in turn may lead to skewed conclusions about the population’s characteristics or opinions.

In the context of our exercise, the employees who are not present at the health fair have no chance of being selected for the survey, introducing a potential bias. This is particularly problematic if the demographic that arrives later, or not at all, has different views about the health-related programs. To avoid sampling bias, researchers need to use strategies that ensure all relevant segments of the population are fairly represented, which might mean employing a different sampling method or adjusting the systematic approach to account for potential patterns in the population.

Representative Sample

A representative sample accurately mirrors the diversity and distribution of the population from which it was drawn. In other words, it should reflect all significant subgroups in the population with respect to the variable being studied. Having a representative sample is critical for the validity of survey results, as it ensures the conclusions drawn can be generalized to the whole population.

In the exercise, because the sample is drawn from a group of individuals who may share certain characteristics—such as being able to attend the health fair early—the resulting data may not represent the entire employee base's opinions. To improve representativeness, multiple strategies could be used, such as weighing the results based on each subgroup's size or applying stratified random sampling to capture a variety of arrival times and employee roles.