17. Think About a Plan An online advertisement asks you to participate in a survey. The survey asks how much time you spend online each week. What sampling method is the survey using? Identify any bias in the sampling method.

    • What population is likely to see the survey?
    • What population is likely to respond to the survey?

Suppose you are conducting a survey about careers. Write a survey question using each of the following biases.

18. leads people to a particular response
19. does not provide enough information
20. combines two or more issues
21. is too wordy or confusing
22. 1. Data Collection Write a survey question to find out the number of students at your school who plan to continue their education after high school.
    2. Describe the sampling method you would use.
    3. Conduct your survey.
23. Entertainment A magazine publisher mails a survey to every tenth person on a subscriber list. The survey asks for three favorite leisure activities. What sampling method is the survey using? Identify any bias in the sampling method.

Margin of Error When you take a random sample of size n from a large population, the sample has a margin of error of approximately ± 1 n . plus minus , fraction 1 , over square root of bold italic n end fraction , .

Approximate the margin of error for each sample.

24. In 2007, the U.S. Mint began issuing one-dollar coins featuring the images of the nation's Presidents. In a survey, 76% of 2431 U.S. adults opposed using one-dollar coins. (Source: The Harris Poll #41, April 14, 2008. Copyright © 2008 Harris Interactive, Inc.)
25. In 2008, tax rebate checks were sent to many American tax payers. In a poll, 45% of 2529 U.S. adults said they felt the rebate program would help stimulate the U.S. economy. (Source: Rebate Checks: No Economic Stimulus, September 10, 2008. Copyright © 2008 Harris Interactive, Inc.)

Margin of Error Interval You can use the margin of error ME to find an interval that is likely to contain the result you would get if you asked the entire population. If the percentage found from a survey is p, the percentage from the total population is likely to be between p − M E bold italic p minus m e  and p + ME. For each margin of error, find an interval that is likely to contain the result from the total population given that the result from the survey is p = 42%.

26. M E = ± 8 % m e equals plus minus 8 percent
27. M E = ± 5 % m e equals plus minus 5 percent
28. M E = ± 1 % m e equals plus minus 1 percent
29. M E = ± 3 . 5 % m e equals plus minus 3 . 5 percent
30. Sample Size If you know the margin of error for a sample, you can find the size of the sample by solving for n. Find the sample size for Exercises 26–29.
31. Writing A margin of error is determined by the sample size. As the sample size increases, the margin of error decreases. How is the margin of error affected if you double the sample size? Explain.

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