(b) Suppose the researcher wants to estimate the mean with a margin of error of no more than $20 with 99% confidence. This could be challenging, though, because the typical American tends to give anywhere from $0 to $216. What is the minimum number of people he should survey? (Use a table or technology.)

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### Estimating the Mean Donation Amount for Political Causes

A researcher aims to estimate the average amount of money that a typical American donates to their favorite politicians or political causes.

#### (a) Determining the Sample Size for 99% Confidence

The researcher seeks to estimate the mean donation amount with 99% confidence. From the given options, they need to choose a sample size that would yield the smallest margin of error. The provided choices and the selection by the researcher are:

- 5
- 17
- 23
- 38 ✔

The researcher has selected a sample size of 38, which would yield the smallest margin of error with 99% confidence.

#### (b) Calculating the Minimum Sample Size for a Specific Margin of Error

Suppose the goal is to estimate the mean donation amount with a margin of error of no more than $20, maintaining a 99% confidence level. This estimation is challenging since the typical American donation amount ranges from $0 to $216. The task is to determine the minimum number of people the researcher should survey.

- The required minimum sample size (n) can be found using statistical tables or technology.

#### Additional Resources

- **Need Help?** (Button): Directs to additional guidance or resources.
- **Use SALT** (Button): Likely to be a tool for statistical analysis.

This information guides researchers and students through calculating appropriate sample sizes for accurate, confident estimations in statistical studies related to donation behaviors.
Transcribed Image Text:### Estimating the Mean Donation Amount for Political Causes A researcher aims to estimate the average amount of money that a typical American donates to their favorite politicians or political causes. #### (a) Determining the Sample Size for 99% Confidence The researcher seeks to estimate the mean donation amount with 99% confidence. From the given options, they need to choose a sample size that would yield the smallest margin of error. The provided choices and the selection by the researcher are: - 5 - 17 - 23 - 38 ✔ The researcher has selected a sample size of 38, which would yield the smallest margin of error with 99% confidence. #### (b) Calculating the Minimum Sample Size for a Specific Margin of Error Suppose the goal is to estimate the mean donation amount with a margin of error of no more than $20, maintaining a 99% confidence level. This estimation is challenging since the typical American donation amount ranges from $0 to $216. The task is to determine the minimum number of people the researcher should survey. - The required minimum sample size (n) can be found using statistical tables or technology. #### Additional Resources - **Need Help?** (Button): Directs to additional guidance or resources. - **Use SALT** (Button): Likely to be a tool for statistical analysis. This information guides researchers and students through calculating appropriate sample sizes for accurate, confident estimations in statistical studies related to donation behaviors.
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