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

```
• 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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```   _____    ______    ____       ___      _____
/ ___//  /_   _//  |  _ \\    / _ \\   / ____||
\___ \\   -| ||-   | |_| ||  / //\ \\ / //---`'
/    //   _| ||_   | .  //  |  ___  ||\ \\___
/____//   /_____//  |_|\_\\  |_||  |_|| \_____||
`-----`    `-----`   `-` --`  `-`   `-`   `----`

```
• 16. Biased Questions about Solar Panels

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

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```           _    _     ______   __   __   _    _
___   | || | ||  /_   _//  \ \\/ // | || | ||
/   || | || | ||  `-| |,-    \ ` //  | || | ||
| [] || | \\_/ ||    | ||      | ||   | \\_/ ||
\__ ||  \____//     |_||      |_||    \____//
-|_||   `---`      `-`'      `-`'     `---`
`-`
```
• 17. Biased Question about Community Service

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

• Worked-Out Solution

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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```  _____    _    _               _____    __   _
|__  //  | || | ||   ____     |  ___|| | || | ||
/ //   | || | ||  |    \\   | ||__   | '--' ||
/ //__  | \\_/ ||  | [] ||   | ||__   | .--. ||
/_____||  \____//   |  __//   |_____|| |_|| |_||
`-----`    `---`    |_|`-`    `-----`  `-`  `-`
`-`
```
• 18. Biased Questions about Recycling

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

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```  _____     ______    _  __    _____