Problem 19 - Prealgebra

Question

A real estate agent surveys people about their housing preferences at an open house for a luxury townhouse. Which is the best explanation for why the results of this survey might NOT be valid? A The survey is biased because the agent should have conducted the survey by telephone. B The survey is biased because the sample consisted of only people who already are interested in townhouses. C The survey is biased because the sample was a voluntary response sample. D The survey is biased because the agent should have conducted the survey at a single-family home.

Step-by-Step Solution

Answer

The survey is biased because the sample consisted of only people who are interested in townhouses (Option B).

Step 1: Understanding the Survey Bias

Bias in a survey occurs when the participants included in the survey do not represent the entire population causing the results to be skewed.

Step 2: Analyzing the Survey Location

The survey was conducted at an open house for a luxury townhouse, so the participants were likely already interested or inclined towards townhouses, leading to a biased sample.

Step 3: Evaluate the Survey Sampling Method

The sample consisted of volunteers who chose to attend the open house, which by itself is a form of biased sampling known as a voluntary response sample. This might not represent the broader population's preferences.

Step 4: Eliminate Irrelevant Options

Option A suggests surveys should be done by telephone, and option D suggests a different location for the survey. These options do not address the core issue of sample bias already present due to the location and voluntary nature of the participants.

Step 5: Identify the Best Explanation for Bias

Given the location and nature of the survey, the most compelling explanation of bias is option B. The survey sample is comprised only of people who are interested in townhouses, thus not representative of the broader population's housing preferences.

Key Concepts

Sampling Methods

In surveys, choosing the right sampling method is crucial for accurate results. Sampling methods are techniques used to select a subset of individuals from a population to participate in a survey. The goal is to represent the entire population accurately. There are several types of sampling methods, including:

• Random Sampling: Every individual has an equal chance of being selected. This method reduces bias and is usually considered the gold standard in surveys.
• Systematic Sampling: Selection follows a specific system, like choosing every 10th person on a list. It is straightforward but can introduce bias if the list is ordered in some way that affects the results.
• Stratified Sampling: The population is divided into subgroups, or "strata," and samples are taken from each stratum. This ensures representation across different key characteristics.
• Voluntary Response Sampling: Participants choose themselves to take part. This method can introduce significant bias, as those with strong opinions are more likely to participate.

Choosing an inappropriate sampling method can lead to biased results, as seen with the voluntary response sampling in the real estate agent's survey.

Voluntary Response

Voluntary response samples are a specific type of sampling method where participants actively choose to take part in a survey. This can lead to significant bias because:

• Only individuals with strong opinions or interests in the topic tend to respond, skewing the results.
• Participants might not reflect the diversity of the overall population.
• It can result in overrepresentation of specific groups within the survey responses.

In the case of the real estate agent’s survey, the participants were attendees of a luxury townhouse open house. This choice of location meant that only those already interested in townhouses were likely to participate, exemplifying the issues with voluntary response sampling.

Population Representation

Population representation in surveys ensures that the data collected reflects the entire group's characteristics and preferences. A well-represented sample considers various demographics, such as age, gender, income, and location.
When a sample is not representative, the conclusions drawn from the survey may not apply to the broader population, leading to "survey bias." This is precisely what happened in the real estate agent's survey. By sampling only those already interested in luxury townhouses, the survey did not capture the housing preferences of people who might prefer other types of dwellings, like single-family homes or apartments.
A representative survey would have included a broader range of participants, ensuring a more accurate depiction of the overall housing preferences.

Survey Analysis

Survey analysis is the process of examining and interpreting the data collected from a survey. It involves looking at the survey's design, the methods used, and the results obtained. Here are key elements to consider:

• Understanding the Sample: Analyze if the sample is representative of the population.
• Identifying Bias: Check for any forms of bias introduced by sampling methods such as voluntary response or convenience sampling.
• Interpreting Results: Look for patterns in the data and consider how they reflect the broader population.
• Making Improvements: Suggest changes in survey design to enhance accuracy in future surveys.

The survey by the real estate agent had a biased sample and, therefore, its analysis would be skewed. The voluntary response nature and the location-specific sampling meant that the results primarily reflected the opinions of those already inclined towards luxury townhouses. A better approach would have been to use a probability sampling method to capture a wider array of opinions.