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

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

```
• 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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``` _    _    __   __    _  _      ___      ______
| \  / ||  \ \\/ //  | \| ||   / _ \\   /_   _//
|  \/  ||   \ ` //   |  ' ||  | / \ ||    | ||
| .  . ||    | ||    | .  ||  | \_/ ||   _| ||
|_|\/|_||    |_||    |_|\_||   \___//   /__//
`-`  `-`     `-`'    `-` -`    `---`    `--`

```
• 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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```   _____    ______              _____     _  _