n =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
#### Required Sample Size:
\[ n = \_\_\_\_\_ \]
To calculate the required sample size when you have no reasonable preliminary estimation for the population proportion and you would like to be 90% confident that your estimate is within 3.5% of the true population proportion, you can use the formula for sample size in estimating population proportions:
\[ n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right) \]
Where:
- \( Z \) is the Z-value (Z-score) corresponding to your desired confidence level (for 90% confidence, Z ≈ 1.645).
- \( p \) is the estimated population proportion (since there is no preliminary estimate, use \( p = 0.5 \) for maximum variability).
- \( E \) is the margin of error (in this case, 3.5% or 0.035).
By substituting these values into the formula, you can determine the required sample size \( n \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2f87264-31b7-42a7-8a6c-1a7d396f05e3%2F46f2e82c-d65e-4b4a-ae9a-069019958e3d%2Fts279y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining Sample Size for Population Proportion Estimation
#### Problem Statement:
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 90% confident that you estimate is within 3.5% of the true population proportion. How large of a sample size is required?
#### Hint:
[Video Tutorial](#)
#### Required Sample Size:
\[ n = \_\_\_\_\_ \]
To calculate the required sample size when you have no reasonable preliminary estimation for the population proportion and you would like to be 90% confident that your estimate is within 3.5% of the true population proportion, you can use the formula for sample size in estimating population proportions:
\[ n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right) \]
Where:
- \( Z \) is the Z-value (Z-score) corresponding to your desired confidence level (for 90% confidence, Z ≈ 1.645).
- \( p \) is the estimated population proportion (since there is no preliminary estimate, use \( p = 0.5 \) for maximum variability).
- \( E \) is the margin of error (in this case, 3.5% or 0.035).
By substituting these values into the formula, you can determine the required sample size \( n \).
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