In a Harris poll, adults were asked if they are in favor of abolishing the penny. Among the...

Question:

In a Harris poll, adults were asked if they are in favor of abolishing the penny. Among the responses, {eq}1290 {/eq} answered "no" , {eq}454 {/eq} answered "yes", and {eq}400 {/eq} had no opinion. What is the sample portion of yes responses, and what notation is used to represent it? Choose the correct answer below:

(A) {eq}p = 0.260 {/eq}. The symbol p is used to represent a sample proportion.

(B) {eq}p = 0.212 {/eq}. The symbol p is used to represent a sample proportion.

(C) Modifying Above p with {eq}\hat p = 0.212 {/eq}. The symbol Modifying Above p with {eq}\hat p {/eq} is used to represent a sample proportion.

(D) Modifying Above p with {eq}\hat p = 0.260 {/eq}. The symbol Modifying Above p with {eq}\hat p {/eq} is used to represent a sample proportion.

Proportion

The sample proportion is the number of observations corresponding to a certain event divided by total number of outcomes in sample space.

{eq}p = \dfrac{{n\left( A \right)}}{n} {/eq}

Answer and Explanation:

Given Information:

In a Harris poll, adults were asked if they are in favor of abolishing the penny. Among the responses,

1290 answered "no" , 454 answered "yes", and 400 had no opinion

The Sample size of poll is given by:

{eq}\begin{align*} n &= 1290 + 400 + 450\\ n &= 2140 \end{align*} {/eq}

The Sample size of poll is 2140.

The Proportion of yes responses is given by:

{eq}\begin{align*} p &= \dfrac{{454}}{{2140}}\\ p &= 0.21214 \approx 0.212 \end{align*} {/eq}

The Proportion of yes responses is 0.212 and is denoted by p.

Hence Option (b) is the correct answer.


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What is a Proportion in Math? - Definition & Practice Problems

from High School Algebra I: Help and Review

Chapter 23 / Lesson 15
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