Answered: A national polling agency conducted a…

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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Question

A national polling agency conducted a survey based on a random sample of Americans. The poll finds that 26% of Americans approve of the job that the President is doing; the poll has a margin of error of 8% (assuming a 95% degree of confidence).

Step 3 of 3:

What was the minimum size of the sample for this poll? Round your answer up to the nearest whole number.

Expert Solution

Step 1: We will write the given things

To calculate the minimum sample size required for a given margin of error, confidence level, and population proportion, you can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

n is the minimum sample size.
Z is the Z-score corresponding to the desired confidence level (for a 95% confidence level, Z is approximately 1.96).
p is the estimated proportion of the population (in this case, 0.26 for 26% approval).
E is the margin of error (in this case, 0.08 for 8%).