Answered: Among the 34,506 people who responded,…

Name: An online site presented this question, "Would the recent norovirus o
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Description: An online site presented this question, "Would the recent norovirus outbreak deter you from taking a cruise?" Among the 34,506 people who responded, 63% answered "yes." Use the sample data to construct a 95% confidence interval estimate for th

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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An online site presented this question, "Would the recent norovirus outbreak deter you from taking a cruise?" Among the 34,506 people who responded, 63% answered "yes."

Use the sample data to construct a 95% confidence interval estimate for the proportion of the population of all people who would respond "yes" to that question.

Does the confidence interval provide a good estimate of the population proportion?

Expert Solution

Step 1

Given data:

Total number of people who responded for the question presented by online site, n = 34506.

Out of those, Percentage of people who responded yes for the question presented by online site = 63%.

The degree of confidence is c = 95% or 0.95

For the 95% confidence interval, the level of significance is:

$\begin{array}{rcl} α & = & 1 - c \\ = & 1 - 0.95 \\ = & 0.05 \end{array}$

Let p be the population proportion of all people who would response yes to that question.

Let $\hat{p}$ be the estimated proportion of people who responded yes for the question presented by online site, that is,

$\hat{p} = 0.63$

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