Answered: he brand manager for a brand of…

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

The brand manager for a brand of toothpaste must plan a companion to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 95% confident that his estimate is within six percentage points of the true population percentage?

Expert Solution

Step 1

Given Information:

Confidence level = 95% = 0.95

Significance level $α = 1 - 0.95 = 0.05$

Margin of Error (E) = 6% = 0.06

Required: To determine the sample size

Nothing is known about the population proportion $p$ of percentage of adults who have heard of the brand:

Assume $p$ = 0.50

Sample size is obtained using the formula:

$n = {(\frac{z_{α / 2}}{E})}^{2} p (1 - p)$

where, $z_{α / 2}$ is the critical value at $\frac{0.05}{2} = 0.025$ significance level.

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