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9.4 Describing by Sampling

9.4 Describing by Sampling
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  • 13. Alternative Energy Survey Sample Size (95% Confidence Level, 3% Margin of Error)

    You work for a research company. You want to determine whether U.S. adults support more funding for alternative energy. Using the Sample Size Calculator, choose a 95% confidence level and a 3% margin of error. How many people should you survey to obtain reliable results? (See Example 5.)

    • Worked-Out Solution

      Using the Sample Size Calculator located in Tools, you can see that you need to survey 1068 people to obtain reliable results.

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      ______     ___     ______     ______    _  _   
     /_   _//   / _ \\  |      \\  /_   _//  | \| || 
       | ||    | / \ || |  --  //   -| ||-   |  ' || 
      _| ||    | \_/ || |  --  \\   _| ||_   | .  || 
     /__//      \___//  |______//  /_____//  |_|\_|| 
     `--`       `---`   `------`   `-----`   `-` -`  
                                                     
    
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  • 14. Alternative Energy Survey Sample Size, (99% Confidence Level, 3% Margin of Error)

    You work for a research company. You want to determine whether U.S. adults support more funding for alternative energy. Using the Sample Size Calculator, choose a 99% confidence level and a 3% margin of error. How many people should you survey to obtain reliable results? Compare this sample size to the sample from Exercise 13. What happens when the confidence level increases? Explain. (See Example 5.)

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      _____     _____    _    _     ______   _    _   
     |__  //   |  ___|| | |  | ||  /_   _// | |  | || 
       / //    | ||__   | |/\| ||   -| ||-  | |/\| || 
      / //__   | ||__   |  /\  ||   _| ||_  |  /\  || 
     /_____||  |_____|| |_// \_||  /_____// |_// \_|| 
     `-----`   `-----`  `-`   `-`  `-----`  `-`   `-` 
                                                      
    
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  • 15. Alternative Energy Survey Sample Size (95% Confidence Level, 5% Margin of Error)

    You work for a research company. You want to determine whether U.S. adults support more funding for alternative energy. Using the Sample Size Calculator, choose a 95% confidence level and a 5% margin of error. How many people should you survey to obtain reliable results? Compare this sample size to the sample size from Exercise 13. What happens when the margin of error increases? Explain. (See Example 5.)

    • Worked-Out Solution

      Using the Sample Size Calculator located in Tools, you can see that you need to survey 385 people to obtain reliable results.

      Notice that when the margin of error increases, the sample size needed decreases.

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      _____    _    _     _  _    __   __   _____    
     |__  //  | || | ||  | \| ||  \ \\/ // |  __ \\  
       / //   | || | ||  |  ' ||   \ ` //  | |  \ || 
      / //__  | \\_/ ||  | .  ||    | ||   | |__/ || 
     /_____||  \____//   |_|\_||    |_||   |_____//  
     `-----`    `---`    `-` -`     `-`'    -----`   
                                                     
    
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  • 16. Biased Questions about Solar Panels

    Determine which question might produce biased results. Explain. (See Example 6.)

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      _____    __   __    _____      ___       _____  
     |__  //   \ \\/ //  |__  //    / _ \\    / ___// 
       / //     \ ` //     / //    / //\ \\   \___ \\ 
      / //__     | ||     / //__  |  ___  ||  /    // 
     /_____||    |_||    /_____|| |_||  |_|| /____//  
     `-----`     `-`'    `-----`  `-`   `-` `-----`   
                                                      
    
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  • 17. Biased Question about Community Service

    Determine which question might produce biased results. Explain. (See Example 6.)

    • Worked-Out Solution

      Sample answer:

      The first question could produce biased results because it states that the policy is unfair and the project is time-consuming whereas the second question does not offer an opinion and is more impartial.

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     _    _    _    _     ______    ______    ____    
    | || | || | || | ||  /_   _//  /_   _//  |  _ \\  
    | || | || | || | ||    | ||     -| ||-   | |_| || 
    | \\_/ || | \\_/ ||   _| ||     _| ||_   | .  //  
     \____//   \____//   /__//     /_____//  |_|\_\\  
      `---`     `---`    `--`      `-----`   `-` --`  
                                                      
    
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  • 18. Biased Questions about Recycling

    Determine which question might produce biased results. Explain. (See Example 6.)

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      ______    _____     _____      ___     ______   
     /_   _//  |  ___||  /  ___||   / _ \\  |      \\ 
     `-| |,-   | ||__   | // __    | / \ || |  --  // 
       | ||    | ||__   | \\_\ ||  | \_/ || |  --  \\ 
       |_||    |_____||  \____//    \___//  |______// 
       `-`'    `-----`    `---`     `---`   `------`  
                                                      
    
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