Question

An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2 -minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey every 10 th person on the line for the roller coaster, starting from a randomly selected individual. a) What kind of sample is this? b) What is the sampling frame? c) Is it likely to be representative?

Short answer

a) Systematic sample. b) People in line for the ride. c) Likely representative if individuals in line are randomly distributed.

Step-by-step solution

Identify the Type of Sample

The exercise describes that every 10th person in line is surveyed, starting from a random individual. This is known as a systematic sample. In a systematic sampling method, a random starting point is selected, and samples are taken at regular intervals from there.

Define the Sampling Frame

The sampling frame refers to the actual list or population from which the sample is drawn. In this scenario, the sampling frame would be all the people who are standing in line for the roller coaster at the time when the survey is conducted.

Evaluate Representativeness

To conclude if the sample is likely to be representative, consider how the selection method (every 10th person) could introduce bias. While systematic sampling can be representative, if there is any pattern or periodicity in the line that correlates with riders' preferences or demographics, the sample might not capture such patterns accurately. However, assuming a random distribution of people in line, it is likely to be representative of the people waiting at that time.

Key concepts

Sampling Frame

When we talk about the sampling frame, it's essential to understand that it is the list or group that the sample is drawn from. In this instance, the sampling frame consists of all the people who are currently waiting in line for the roller coaster.
Without an accurate sampling frame, you might miss out on segments of the population you want to study or accidentally include those you didn't intend to.

• The sampling frame should be carefully defined to reflect the entirety of the population in question.
• It must be accessible for selection to ensure every part of the population can be potentially included in the survey.

An inaccurate sampling frame may lead to bias or errors in your survey results, as you might not be reaching the right individuals or a complete set of the audience. In this example, the sampling frame captures only those who were in line during the survey period, meaning it could potentially miss opinions from people who avoided the line due to long wait times.

Sample Representativeness

One critical aspect of conducting surveys is ensuring that your sample is representative of the whole population you want to understand.
A representative sample accurately reflects the various characteristics and responses of the entire group. Systematic sampling, where you survey every 10th person in line, is a good strategy to achieve representativeness, provided that the line setup does not inherently bias the outcomes.
Here are some factors that can help assure representativeness:

• Randomization: Starting the sample with a randomly selected individual helps in reducing selection biases.
• Interval Sampling: Having a regular interval (like every 10th person) aids in spreading the responses evenly across the timeframe.

However, potential issues include any undetected pattern in the queue that could skew results based on timing or sequence. For instance, if a particular type of visitor arrives at specific intervals, the sample might not reflect other visitor types. It's crucial to be mindful of such instances to maintain high precision in survey outcomes.

Survey Methodology

In survey methodology, the planning and execution of the survey process are paramount to acquiring reliable data. The method you choose, like systematic sampling, directly influences the quality and applicability of your survey results.
This systematic approach involves a starting point chosen at random, then continuing to select at consistent steps—in this case, every 10th person. Such a methodology helps eliminate some biases and keeps the survey process structured and straightforward.

• Advantages: It's simpler and quicker to execute compared to other methods, and it works well when the population is homogenous.
• Disadvantages: If the population shows a hidden pattern, this method might overlook it, leading to skewed data.

Every survey methodology comes with its potential pitfalls. Therefore, before applying systematic sampling, ensure the absence of any hidden patterns that could affect your results. Proper execution of your survey methodology can help determine legitimate trends and provide insightful data reflecting the population's true sentiments.