**Question 7**In a recent poll, 450 people were asked if they liked dogs, and 65% said they did. Find the Margin of Error for this poll, at the 90% confidence level. Give your answer to four decimal places if possible. [Text Box for Response][Submit Question Button]There are no graphs or diagrams in the image.

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Description: **Question 7**In a recent poll, 450 people were asked if they liked dogs, and 65% said they did. Find the Margin of Error for this poll, at the 90% confidence level. Give your answer to four decimal places if possible. [Text Box for Response][Submit

Answered: In a recent poll, 450 people were asked…

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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Step 1

The margin of error provides the percentage difference between a true population value and the estimated value.

The margin of error defines as

${MOE}_{γ} = z_{γ} \frac{σ}{\sqrt{n}}, σ is the standard deviation, n is the sample size, z_{γ} is the quantile, γ is the confidence level.$

Step 2

Suppose, p be the proportion of people like dogs.

Given that 65% of people like dogs.

$p = 0.65$

450 samples are taken,

then n=450.

The standard deviation is

$\begin{array}{rcl} σ & = & \sqrt{np (1 - p)} \\ = & \sqrt{450 \times 0.65 \times (1 - 0.65)} \\ = & \sqrt{102.375} \\ = & 10.1181 \end{array}$

From the z table

$\begin{array}{rcl} z_{γ} & = & z_{0.90} \\ = & 1.646 \end{array}$

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