Ron Larson
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1.3 Using Percent

1.3 Using Percent
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  • 1. American Men's Opinion about the Funding of Stem Cell Research

    The bar graph shows the results of a poll of adult Americans about federal government funding of stem cell research. There are about 117,000,000 adult American men. About how many of these men think the federal government should fund stem cell research? (See Example 1.)

    • Worked-Out Solution

      In the poll, 58% of the men think that the government should fund stem cell research. If this is representative of the entire population, then you can estimate that

      believe that the federal government should fund stem cell research.

      This type of projection is called "statistical inference." (See Chapter 9.) The basic concept is to randomly select a sample from a large population and then "infer" that the large population has the same characteristics as the sample. In statistics, it is possible to verify that this process is mathematically valid. There are still, however, two huge problems with using a poll to determine information about a large population. (1) The sample must be randomly chosen and this is difficult. (2) The way the questions are worded has a tremendous effect on how people answer. For instance, people would likely answer the following questions differently.

      "Do you agree that stem cell research is morally justifed because it can find cures that can't be found in other ways?"

      "Do you think the the federal government should fund stem cell research?"

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     __   _     _____     ____       ___      ______  
| || | ||  |  ___||  |  _ \\    / _ \\   /_   _// 
| '--' ||  | ||__    | |_| ||  / //\ \\    | ||   
| .--. ||  | ||__    | .  //  |  ___  ||  _| ||   
|_|| |_||  |_____||  |_|\_\\  |_||  |_|| /__//    
`-`  `-`   `-----`   `-` --`  `-`   `-`  `--`
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  • 2. American Women's Opinion about the Funding of Stem Cell Research

    The bar graph shows the results of a poll of adult Americans about federal government funding of stem cell research. There are about 123,000,000 adult American women. About how many of these women think the federal government should fund stem cell research? (See Example 1.)

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     _    _      ___               _    _     _____   
| || | ||   / _ \\      ___   | || | ||  / ____|| 
| || | ||  | / \ ||    /   || | || | || / //---`' 
| \\_/ ||  | \_/ ||   | [] || | \\_/ || \ \\___   
 \____//    \___//     \__ ||  \____//   \_____|| 
  `---`     `---`       -|_||   `---`     `----`  
                         `-`
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  • 3. Public Opinion about the Funding of Stem Cell Research

    The bar graph shows the results of a poll of adult Americans about federal government funding of stem cell research. There are about 117,000,000 adult American men and about about 123,000,000 adult American women. Describe two ways to find how many American adults have no opinion about federal government funding of stem cell research. Do both ways result in the same answer? Explain. (See Example 1.)

    • Worked-Out Solution

      One way is to add the male and female population

      and then estimate (from the graph) that 4% of these have no opinion.

      A second way is to separately find the number of males and females who have no opinion and add the two results.

      This implies that

      have no opinion about federal funding of stem cell research.

      The two methods give different results. The reason for the difference is probably due to round-off error when summarizing the poll results to make the graph.

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     __   __     ___     _    _     ______   _    _   
 \ \\/ //   / _ \\  | |  | ||  /_   _// | \  / || 
  \   //   | / \ || | |/\| ||   -| ||-  |  \/  || 
  / . \\   | \_/ || |  /\  ||   _| ||_  | .  . || 
 /_//\_\\   \___//  |_// \_||  /_____// |_|\/|_|| 
 `-`  --`   `---`   `-`   `-`  `-----`  `-`  `-`
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  • 4. Public Opinion about the Funding of Stem Cell Research

    The bar graph shows the results of a poll of adult Americans about federal government funding of stem cell research. Are the results for men significantly different than the results for women? Explain. (See Example 1.)

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     _    _    __   __             __   __    _  _   
| \  / ||  \ \\/ //   ____     \ \\/ //  | \| || 
|  \/  ||   \ ` //   |    \\    \ ` //   |  ' || 
| .  . ||    | ||    | [] ||     | ||    | .  || 
|_|\/|_||    |_||    |  __//     |_||    |_|\_|| 
`-`  `-`     `-`'    |_|`-`      `-`'    `-` -`  
                     `-`
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  • 5. Estimating the Population of a City

    The circle graph shows the results of a poll of adult Americans about the moral acceptability of stem cell research. In a city, 412,230 adults think that stem cell research is morally wrong. Estimate the population of the city. (See Example 2.)

    • Worked-Out Solution

      The poll indicates that 32% of the population believe that stem cell research is morally wrong. So, you need to answer the question

      Because 32% is about   1 divided by 3 , this is roughly equivalent to solving the equation

      So, you can estimate that the city has a population of about

      or roughly "one and a quarter million" people.

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      _____      ___      ______    _____     _____   
 |__  //    / _ \\   /_____//  |  ___||  |__  //  
   / //    / //\ \\  `____ `   | ||__      / //   
  / //__  |  ___  || /___//    | ||__     / //__  
 /_____|| |_||  |_|| `__ `     |_____||  /_____|| 
 `-----`  `-`   `-`  /_//      `-----`   `-----`  
                     `-`
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  • 6. Public Opinion about Stem Cell Research

    The circle graph shows the results of a poll of adult Americans about the moral acceptability of stem cell research. How many adults from the city in Exercise 5 think stem cell research is morally acceptable? (See Example 2.)

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                 ___    __    __    _____     _____   
    ___     / _ \\  \ \\ / //  |  ___||  /  ___|| 
   /   ||  / //\ \\  \ \/ //   | ||__   | // __   
  | [] || |  ___  ||  \  //    | ||__   | \\_\ || 
   \__ || |_||  |_||   \//     |_____||  \____//  
    -|_|| `-`   `-`     `      `-----`    `---`   
     `-`
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  • 7. Conducting a Poll about Stem Cell Research

    Conduct a poll on stem cell research by asking at least 30 people for their opinion. Compare your results to the bar graph and circle graph shown below.


    • Worked-Out Solution

      Two primary things to keep in mind while conducting a poll are:

      1. Make sure that your sample is randomly chosen.

      1. Word each question in a neutral manner that does not lead the subject to answer one way or the other.

      Even with these guidelines, you still might not duplicate the results of the polls shown in the bar graph and the circle graph. Opinions about stem cell research vary regionally in the United States and your results could depend on the location of the people who answered your poll.

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      _____      ___      ______   _    _     ______  
 / ____||   / _ \\   /_____// | || | ||  /_   _// 
/ //---`'  | / \ ||  `____ `  | || | ||    | ||   
\ \\___    | \_/ ||  /___//   | \\_/ ||   _| ||   
 \_____||   \___//   `__ `     \____//   /__//    
  `----`    `---`    /_//       `---`    `--`     
                     `-`
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  • 8. Summarizing Results of a Poll Graphically

    Summarize the results of your poll in Exercise 7 graphically. Explain your choice of graph. (See Example 2.)

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                ______    _____    __   __   __   __  
  ____     /_   _//  / ____||  \ \\/ //  \ \\/ // 
 |    \\    -| ||-  / //---`'   \ ` //    \   //  
 | [] ||    _| ||_  \ \\___      | ||     / . \\  
 |  __//   /_____//  \_____||    |_||    /_//\_\\ 
 |_|`-`    `-----`    `----`     `-`'    `-`  --` 
 `-`
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