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9.4 Describing by Sampling

9.4 Describing by Sampling
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  • 5. Bias in a Dental Survey

    Explain why the sample may be biased. Then explain how to find an unbiased sample. (See Example 3 and Example 4.)

    A research company wants to determine how many people floss their teeth. The company asks a dentist to conduct a survey by randomly selecting patients.

    • Worked-Out Solution

      The sample may be biased because people may lie to their dentists about flossing their teeth. To find an unbiased sample, a dentist should not be the one conducting the survey.

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      _  _     ______   _____      _____    _____    
     | \| ||  /_   _// |  __ \\   |  ___|| |  __ \\  
     |  ' ||   -| ||-  | |  \ ||  | ||__   | |  \ || 
     | .  ||   _| ||_  | |__/ ||  | ||__   | |__/ || 
     |_|\_||  /_____// |_____//   |_____|| |_____//  
     `-` -`   `-----`   -----`    `-----`   -----`   
                                                     
    
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  • 6. Bias in a Survey on Riding a School Bus

    Explain why the sample may be biased. Then explain how to find an unbiased sample. (See Example 3 and Example 4.)

    You want to estimate the number of students in a high school who ride the school bus. You randomly survey 60 seniors.

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     __   __     ___     _    _      ___              
     \ \\/ //   / _ \\  | \  / ||   / _ \\    ____    
      \   //   / //\ \\ |  \/  ||  / //\ \\  |    \\  
      / . \\  |  ___  ||| .  . || |  ___  || | [] ||  
     /_//\_\\ |_||  |_|||_|\/|_|| |_||  |_|| |  __//  
     `-`  --` `-`   `-` `-`  `-`  `-`   `-`  |_|`-`   
                                             `-`      
    
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  • 7. Bias in a Factory Inspection

    Explain why the sample may be biased. Then explain how to find an unbiased sample. (See Example 3 and Example 4.)

    You want to estimate the number of defective items produced by a factory. You randomly inspect 200 items from one of the machines in the factory.

    • Worked-Out Solution

      The sample may be biased because you are only choosing items from one of the machines. That one machine could be producing hardly any defective items or could be producing more defective items than the other machines. To find an unbiased sample, you need to choose items from all of the machines.

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                _____    ______      ___    __    __  
        ___    |  ___|| |      \\   / _ \\  \ \\ / // 
       /   ||  | ||__   |  --  //  / //\ \\  \ \/ //  
      | [] ||  | ||__   |  --  \\ |  ___  ||  \  //   
       \__ ||  |_____|| |______// |_||  |_||   \//    
        -|_||  `-----`  `------`  `-`   `-`     `     
         `-`                                          
    
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  • 8. Bias in a Survey on Renovation

    Explain why the sample may be biased. Then explain how to find an unbiased sample. (See Example 3 and Example 4.)

    A college wants to determine whether to renovate the gym or the science lab. The college asks you to conduct a survey. You randomly survey 30 students leaving a science club meeting.

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      _____     ______   __   _     ______    ______  
     / ____||  /_   _// | || | ||  /_   _//  /_____// 
    / //---`'   -| ||-  | '--' ||   -| ||-   `____ `  
    \ \\___     _| ||_  | .--. ||   _| ||_   /___//   
     \_____||  /_____// |_|| |_||  /_____//  `__ `    
      `----`   `-----`  `-`  `-`   `-----`   /_//     
                                             `-`      
    
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  • 9. Bias in a Gun Control Survey

    Explain why the sample may be biased. Then explain how to find an unbiased sample. (See Example 3 and Example 4.)

    A radio station wants to determine how many people in the listening area support gun control laws. The station asks listeners to call in and answer the survey.

    • Worked-Out Solution

      The sample may be biased because people who have a very strong opinion will call in. To find an unbiased sample, the radio station should survey random people in the listening area.

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      _  __   _    _     ______   _    _    _    _   
     | |/ // | || | ||  /_   _// | || | || | |  | || 
     | ' //  | || | ||    | ||   | || | || | |/\| || 
     | . \\  | \\_/ ||   _| ||   | \\_/ || |  /\  || 
     |_|\_\\  \____//   /__//     \____//  |_// \_|| 
     `-` --`   `---`    `--`       `---`   `-`   `-` 
                                                     
    
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  • 10. Bias in a Survey on the Use of Tax Dollars to Build a Stadium

    Explain why the sample may be biased. Then explain how to find an unbiased sample. (See Example 3 and Example 4.)

    A city wants to determine whether the residents of the city favor using tax dollars to build a new baseball stadium. The city asks you to conduct a survey. You randomly survey people entering a sporting goods store.

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      _  __     ___               __   __    ____    
     | |/ //   / _ \\    ____     \ \\/ //  |  _ \\  
     | ' //   | / \ ||  |    \\    \ ` //   | |_| || 
     | . \\   | \_/ ||  | [] ||     | ||    | .  //  
     |_|\_\\   \___//   |  __//     |_||    |_|\_\\  
     `-` --`   `---`    |_|`-`      `-`'    `-` --`  
                        `-`                          
    
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  • 11. Bias in Nursing Home Care Insurance Survey

    Explain why the sample may be biased. Then explain how to find an unbiased sample. (See Example 3 and Example 4.)

    A mayor wants to determine whether residents of a city support a bill providing insurance for nursing home care. The mayor asks you to conduct a survey. You randomly survey residents of five nursing homes in the city.

    • Worked-Out Solution

      The sample may be biased because people living in the nursing homes are more likely to support the bill. To find an unbiased sample, you should survey a random sample of people in the city.

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     _    _      ___      ______   __   __   _    _   
    | \  / ||   / _ \\   /_____//  \ \\/ // | |  | || 
    |  \/  ||  | / \ ||  `____ `    \ ` //  | |/\| || 
    | .  . ||  | \_/ ||  /___//      | ||   |  /\  || 
    |_|\/|_||   \___//   `__ `       |_||   |_// \_|| 
    `-`  `-`    `---`    /_//        `-`'   `-`   `-` 
                         `-`                          
    
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  • 12. Bias in a Survey on Beach Vacations

    Explain why the sample may be biased. Then explain how to find an unbiased sample. (See Example 3 and Example 4.)

    A research company wants to determine how many people in the United States spend at least 1 week at the beach each year. The company surveys residents of California, Florida, and North Carolina.

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     _____       ___     _    _    _    _    _    _   
    |  __ \\    / _ \\  | |  | || | || | || | \  / || 
    | |  \ ||  / //\ \\ | |/\| || | || | || |  \/  || 
    | |__/ || |  ___  |||  /\  || | \\_/ || | .  . || 
    |_____//  |_||  |_|||_// \_||  \____//  |_|\/|_|| 
     -----`   `-`   `-` `-`   `-`   `---`   `-`  `-`  
                                                      
    
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