You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 42%. You would like to be 99% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required? Hint: Video [+]

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### Estimating Sample Size for Population Proportion

To estimate a population proportion, you need to determine the appropriate sample size. Consider the following scenario:

**Scenario:**

- **Population Proportion (p):** Approximately 42%
- **Confidence Level:** 99%
- **Margin of Error:** 2.5%

**Question:**
How large of a sample size is required to ensure your estimate is within 2.5% of the true population proportion with 99% confidence?

**Hint:**
A linked video is provided to assist with this calculation.

**Input Field:**
You are prompted to input the calculated sample size (n) and submit your answer using the "Submit Question" button.

**Note:**
To calculate the sample size, you can use the formula for sample size estimation for proportions:

\[ n = \left( \frac{Z^2 \times p \times (1-p)}{E^2} \right) \]

Where:
- \( Z \) is the Z-score corresponding to the desired confidence level.
- \( p \) is the estimated population proportion.
- \( E \) is the margin of error.

This exercise helps learners apply statistical concepts to real-world data analysis scenarios.
Transcribed Image Text:### Estimating Sample Size for Population Proportion To estimate a population proportion, you need to determine the appropriate sample size. Consider the following scenario: **Scenario:** - **Population Proportion (p):** Approximately 42% - **Confidence Level:** 99% - **Margin of Error:** 2.5% **Question:** How large of a sample size is required to ensure your estimate is within 2.5% of the true population proportion with 99% confidence? **Hint:** A linked video is provided to assist with this calculation. **Input Field:** You are prompted to input the calculated sample size (n) and submit your answer using the "Submit Question" button. **Note:** To calculate the sample size, you can use the formula for sample size estimation for proportions: \[ n = \left( \frac{Z^2 \times p \times (1-p)}{E^2} \right) \] Where: - \( Z \) is the Z-score corresponding to the desired confidence level. - \( p \) is the estimated population proportion. - \( E \) is the margin of error. This exercise helps learners apply statistical concepts to real-world data analysis scenarios.
Title: Determining Sample Size for Estimating a Population Mean

**Problem Statement:**

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately \( \sigma = 76.9 \). You would like to be 95% confident that your estimate is within 5 of the true population mean. How large of a sample size is required?

**Interactive Element:**

- **Hint:**
  - [Video] [
Transcribed Image Text:Title: Determining Sample Size for Estimating a Population Mean **Problem Statement:** You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately \( \sigma = 76.9 \). You would like to be 95% confident that your estimate is within 5 of the true population mean. How large of a sample size is required? **Interactive Element:** - **Hint:** - [Video] [
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