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You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 88%. You would like to be 95% confident that your estimate is within 1% of the true population proportion. How large.of a sample size is required? Hint: Video [+] n=

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 88%. You would like to be 95% confident that your estimate is within 1% of the true population proportion. How large.of a sample size is required? Hint: Video [+] n=

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Educational Website Content** --- ### Estimating a Population Proportion Sample Size To accurately estimate a population proportion, it's essential to determine the appropriate sample size required for the desired level of confidence and precision. Follow the scenario provided below to understand how to calculate the required sample size. --- #### Scenario: You aim to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 88%. You wish to be 95% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required? --- #### Guided Steps: - **Hint**: If you need assistance, refer to the provided **Video [⦿]** for a detailed explanation on calculating sample sizes. #### Calculation: To find the required sample size (\(n\)), you should use the formula for estimating a population proportion with a given confidence level and margin of error. 1. **Population Proportion (p)**: 88% or 0.88 2. **Confidence Level**: 95% (corresponding to a Z-score from the standard normal distribution) 3. **Margin of Error (E)**: 1% or 0.01 The formula to calculate the sample size (\(n\)) is: \[ n = \left( \frac{Z \times \sqrt{p(1-p)}}{E} \right)^2 \] Where \(Z\) is the Z-score corresponding to the desired confidence level (for 95%, \(Z = 1.96\)). --- #### Interactive Input: Enter your calculated sample size in the field below: - **n =** [Submit Question] --- By submitting your answer, you can verify your understanding of sample size estimation and ensure you have mastered the fundamental concepts required for accurate statistics in population studies. --- **Note:** Implementing a proper sample size calculation is crucial to attain reliable and valid results in population proportion estimation.
Transcribed Image Text:**Educational Website Content** --- ### Estimating a Population Proportion Sample Size To accurately estimate a population proportion, it's essential to determine the appropriate sample size required for the desired level of confidence and precision. Follow the scenario provided below to understand how to calculate the required sample size. --- #### Scenario: You aim to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 88%. You wish to be 95% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required? --- #### Guided Steps: - **Hint**: If you need assistance, refer to the provided **Video [⦿]** for a detailed explanation on calculating sample sizes. #### Calculation: To find the required sample size (\(n\)), you should use the formula for estimating a population proportion with a given confidence level and margin of error. 1. **Population Proportion (p)**: 88% or 0.88 2. **Confidence Level**: 95% (corresponding to a Z-score from the standard normal distribution) 3. **Margin of Error (E)**: 1% or 0.01 The formula to calculate the sample size (\(n\)) is: \[ n = \left( \frac{Z \times \sqrt{p(1-p)}}{E} \right)^2 \] Where \(Z\) is the Z-score corresponding to the desired confidence level (for 95%, \(Z = 1.96\)). --- #### Interactive Input: Enter your calculated sample size in the field below: - **n =** [Submit Question] --- By submitting your answer, you can verify your understanding of sample size estimation and ensure you have mastered the fundamental concepts required for accurate statistics in population studies. --- **Note:** Implementing a proper sample size calculation is crucial to attain reliable and valid results in population proportion estimation.
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