### QUESTION 6A manufacturer needs to test to see the proportion of faulty products they produce. How large of a sample must they use to get a 99% confidence interval for this proportion with a width no greater than 14%?---**Explanation:**To determine the appropriate sample size for a confidence interval, consider the following steps:1. **Identify the Desired Confidence Level:** Here, it is 99%.2. **Determine the Maximum Acceptable Width of the Confidence Interval:** In this case, it is 14%.3. **Estimate the Proportion of Faulty Products (p):** - Without a preliminary estimate, use p = 0.5 for the worst-case scenario, as it maximizes the sample size requirement.4. **Use the Equation for Sample Size (n):** The formula for calculating the sample size for a proportion is: \[ n = \left( \frac{Z^2 \cdot p \cdot (1 - p)}{E^2} \right) \] Where: - \( n \) = required sample size - \( Z \) = Z-value (from the Z-table corresponding to the desired confidence level) - \( p \) = estimated proportion of faulty products - \( E \) = maximum acceptable error (half the width of the confidence interval)5. **Find the Z-value for 99% Confidence:** - The Z-value for a 99% confidence level is approximately 2.576.6. **Calculate the Required Sample Size:** - Assuming p = 0.5 and E = 0.07 (since 14% width means ±7%): \[ n = \left( \frac{2.576^2 \cdot 0.5 \cdot (1 - 0.5)}{0.07^2} \right) \] - Simplify the calculation to find n.This step-by-step approach will guide how to determine the necessary sample size to achieve the desired confidence interval.

Given:Width of the interval=14% =0.14The margin of error, i.e, E is…

Answered: ESTION 6 nufacturer needs to test to…

ESTION 6 nufacturer needs to test to see the proportion of faulty products they produce. How large of a sample must the onfidence interval for this proportion with a width no greater than 14%

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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