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# 12.8: Surveys and Samples

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## Learning Objectives

At the end of this lesson, students will be able to:

• Classify sampling methods.
• Identify biased samples.
• Identify biased questions.
• Design and conduct a survey.
• Display, analyze, and interpret statistical survey data.

## Vocabulary

Terms introduced in this lesson:

census
sampling method
representative sample
random sampling
stratified sampling
sample size
bias
biased sample
population
sample
cherry picking
non-response bias
self-selected respondents
poll
survey
biased question
question order
design and conduct a survey
face-to-face interview
survey data

## Teaching Strategies and Tips

Students learn about surveys and samples as ways of collecting information:

• Examples accompany each type of method and help students put them into context.
• Emphasize the advantages and disadvantages of each type of sampling method: census, random, and stratified.

Identify the type of sampling used.

a. A superintendent has a computer generate a list of $100$ teachers from the $10$ schools in her district and interviews them about working conditions.

b. At a certain high school there are $730$ freshmen, $512$ sophomores, $475$ juniors, and $103$ seniors. A reporter from the school newspaper interviews $15$ freshmen, $12$ sophomores, $13$ juniors, and $10$ seniors about their college plans.

c. Around mid-semester, a certain university requires a teacher’s evaluation. A form is given to each student in every class to fill out.

Emphasize that samples consisting of over or under-represented sub-groups are biased.

• Point out that a biased sample does not accurately reflect the spread of people present in the population and, therefore, the sample should not be expected to represent the entire population.

Identify each sample as biased or unbiased. If the sample is biased explain how you would improve your sampling method.

a. County health officials randomly selected non-smokers walking out of a bar. They politely asked every other person whether or not second-hand smoke affects them.

Hint: Possible under-represented group; people who dislike second-hand smoke tend to stay away from bars.

b. At a popular ski resort, people were surveyed about the cafeteria food. The survey was handed out in the cafeteria and was to be mailed in, postage paid. The results were to be published the county newspaper.

Hint: Possible bias includes the voluntary response of the people being surveyed. For example, those who find the time and effort to mail in the survey may be predisposed to a certain opinion.

c. A potato chip manufacturer packaging bags of chips maintains quality control by randomly selecting $100$ bags over the course of $48\;\mathrm{hours}$ and weighs each bag. They then inspect $10$ bags by opening them and tasting the chips.

Hint: No apparent bias.

d. People visiting the website of a popular teen magazine had the option of participating in a poll on whether the legal drinking age should be lowered.

Hint: Possible bias includes the voluntary response of the people being surveyed.

Teachers are encouraged to read and discuss with their students the ways to spot biased questions. See the list following Example 2.

Examine the question for possible bias. If you think the question is biased, indicate how to propose a better question.

a. Given that underage drinking is responsible for $17\%$ of all car accidents, do you think the legal drinking age should be lowered?

Hint: Biased. Possible alternative: “Do you think lowering the legal drinking age is appropriate?”

b. Should corporations that use diesel fuel in their transports, and thus pollute the environment, pay an environmental tax to help clean the air?

Hint: Biased. Possible alternative: “Should corporations using diesel fuel pay an environmental tax?”

c. Are you in favor of continued funding for the high school’s remarkable theater program?

Hint: Biased. Possible alternative: “Do you favor continued funding for the high school theater program?"

d. Do you think all high school students should be required to take a physical education course?

Hint: Likely unbiased.

Use Examples 3 and 4 to demonstrate step-by-step how to conduct a survey.

Use the last part of the lesson to show students how to display, analyze, and interpret survey data. Appropriate ways to display data are: pie-charts and bar-graphs for categorical data; stem-and-leaf plots, histograms, and box-and-whisker plots for numerical data.

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## Date Created:

Feb 22, 2012

Aug 22, 2014
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