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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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**Sample Size Determination for Estimating Proportions**

**Question:**

How many widgets need to be sampled in order to be 98% confident that the error in estimating the true proportion of defective widgets is at most 0.05? Assume you have no idea what the true proportion is.

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**Explanation:**

To solve this problem, we need to determine the sample size required to estimate the proportion of defective widgets with a certain level of confidence and margin of error.

**Variables and Formula:**

1. **Confidence Level (CL):** 98%
2. **Margin of Error (E):** 0.05
3. **Proportion (p):** Since there's no knowledge of the true proportion, p is assumed as 0.5 (maximizing variability).
4. **Z-score:** Corresponding to the 98% confidence level. This is approximately 2.33.

The formula for calculating sample size \( (n) \) when the population proportion is unknown is:

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

**Steps:**

1. **Calculate the Z-score** for 98% confidence.
2. **Apply the formula** using the values of Z, p, and E.

The result will give you the minimum number of widgets needed to be sampled to ensure the desired confidence and accuracy in estimating the proportion of defective widgets.

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