6.6 Analyze Surveys and Samples

Vocabulary

Survey: study of 1+ characteristics of a group

Population: entire group Sample: part of the population Random sample: every member of the

pop. has = chance of being selected Stratified random sample: pop. divided

into groups, members are selected from each group

Vocabulary Systematic sample: rule used to select

members of the pop. Convenience sample: only members of the

pop. who are easily accessible are selected Self-selected sample: members volunteer Representative sample: accurately reflects

the characteristics of a pop. Biased sample: doesn’t represent the pop. Biased question: question that encourages a

particular response

EXAMPLE 1Classify a sampling method

The owners of a company with several factories conduct a survey to determine whether employees are informed about safety regulations. At each factory, 50 employees are chosen at random to complete the survey. Identify the population and classify the sampling method.

EMPLOYEE SAFETY

SOLUTION

The population is all company employees. Because the population is divided into distinct groups (individual factories), with employees chosen at random from each group, the sample is a stratified random sample.

GUIDED PRACTICE

1. WHAT IF? In Example 1, suppose the owners survey each employee whose last name begins with M. Classify the sampling method.

Systematic b/c rule = last name begins w/ M

ANSWER

EXAMPLE 2Identify a potentially biased sample

In Example 1, suppose the owners question 50 workers chosen at random from one factory. Is the method likely to result in a biased sample?

SOLUTION

Workers at other factories may hold significantly different opinions, so the method may result in a biased sample.

EXAMPLE 3Identify potentially biased questions

Tell whether the question is potentially biased. Explain your answer. If the question is potentially biased, rewrite it so that it is not.

Don’t you agree that the voting age should be lowered to 16 because many 16-year-olds are responsible and informed?

a.

Do you think the city should risk an increase in pollution by allowing expansion of the Northern Industrial Park?

b.

EXAMPLE 3Identify potentially biased questions

SOLUTION

This question is biased because it suggests that lowering the voting age is a good thing to do. An unbiased question is “Do you think the voting age should be lowered to 16?”

a.

This question is biased because it suggests that the proposed expansion will be bad for the environment. An unbiased question is “Do you think the city should allow expansion of the Northern Industrial Park?”

b.

GUIDED PRACTICE

2. In a survey about Americans’ interest in soccer, the first 25 people admitted to a high school soccer game were asked, “How interested are you in the world’s most popular sport, soccer?”

ANSWER

Yes. All people sampled were visiting a soccer game, so they may be more likely than the American population to be interested in soccer.

SOCCER

Is the sampling method likely to result in a biased sample? Explain.

a.

GUIDED PRACTICE

Yes. The question suggests that soccer is popular and may encourage respondents to say they are interested in soccer.

“How interested or disinterested are you in soccer?” would be an unbiased way of asking the question.

ANSWER

Is the question potentially biased? Explain your answer. If the question is potentially biased, rewrite it so that it is not.

b.