Problem 27 - BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Question

In Exercises 25–28, explain why the survey question may be biased or otherwise introduce bias into the survey. Then describe a way to correct the flaw. "The tap water coming from our western water supply contains twice the level of arsenic of water from our eastern supply. Do you think the government should address this health problem?"

Step-by-Step Solution

Answer

The survey question is biased because it suggests that the arsenic level in the western water supply constitutes a health problem without providing sufficient information about safe arsenic levels. The question can be corrected by removing the leading wording and providing necessary information for a grounded decision.

Step 1: Identify Bias

Identify the potential bias in the survey question. The question is 'The tap water coming from our western water supply contains twice the level of arsenic of water from our eastern supply. Do you think the government should address this health problem?' is leading the respondent to think of the arsenic levels in the western water supply as a 'health problem', even though no information about safe arsenic levels is given.

Step 2: Determine Corrective Measures

Think about corrective measures to make the question unbiased. Contrasts should be fair and offer all necessary information to make a grounded decision. In this context, it may help to provide information about acceptable arsenic limits in water.

Step 3: Rephrase Question

Rephrase the survey question in a way that minimizes any leading wording and offers necessary information. A possible rephrase of the question could be: 'The tap water coming from our western water supply contains twice the level of arsenic as our eastern supply. Given that the maximum safe level of arsenic in water is X, do you think this issue should be addressed by the government?'

Key Concepts

Statistical Bias Correction

In the world of statistics, bias represents a systematic error that can lead to inaccurate conclusions. Statistical bias correction involves the identification and removal of bias in order to restore the integrity of the data. When a survey question is biased, it can tilt responses in a particular direction, undermining the reliability of the survey's findings.

For instance, if the original question suggests that arsenic levels in the water are definitively a health problem without providing context, this could influence respondents to support government intervention without knowing if action is truly necessary. A crucial step in correcting this bias is by not only rephrasing the question to remove leading language but also by ensuring the information provided is both accurate and sufficient for fair assessment. In the context of arsenic levels in water, imparting knowledge about safe level thresholds is essential for individuals to make an informed response about the necessity of government action.

Question Phrasing in Surveys

The phrasing of questions in surveys is critical to acquiring valid data. Questions must be constructed in a way that is clear, unbiased, and straightforward to avoid directing respondents toward a particular answer. Inaccurate phrasing could distort the survey results and lead to false interpretations. When formulating survey questions, consider neutral wording and ensure it does not inadvertently contain any assumptions or emotive language that could impact responses.

For example, a question that suggests a situation is a 'health problem' without providing supporting evidence can nudge participants toward a specific concern. Instead, presenting facts without any evaluative language allows respondents to process the information independently.

Revising for Neutrality

Revising a question to make it neutral might look like stating the arsenic levels and then asking if the respondent is concerned about these levels, without implicitly suggesting there should be concern.

Acceptable Arsenic Levels in Water

Determining acceptable arsenic levels in drinking water is essential for public health. Arsenic is naturally occurring but can be harmful at high concentrations. Regulatory bodies like the Environmental Protection Agency (EPA) in the United States have set standards for safe levels of arsenic in municipal water supplies.

For example, as of this writing, the EPA has a limit of 10 micrograms per liter (µg/L) as the maximum contaminant level for arsenic in drinking water. Placing this value in survey questions provides a benchmark for the respondents. With such context, people can evaluate if the levels in question are above or below the safety threshold, allowing for a more informed opinion on whether government action should be considered. Understanding these standards is not only vital for survey design but also for public awareness and health decision-making processes.