Chapter 12, Problem 17PTTS

To determine

To find : Whether the proposition will pass or not.

Answer to Problem 17PTTS

No, it cannot be conclude that the proposition will pass because lower range of the vote percentage $\left(66\%\right)$ is lower than the required percentage $\left(66.67\%\right)$ .

Explanation of Solution

Given information : A proposition on a voting ballot needs two thirds of votes to pass. A survey of a random sample of voters finds that $69\%$ of voters plan to vote for the proposition. The survey’s margin of error is $\pm 3\%$ .

Formula used : If the result of the survey is $x\%$ and its margin error is $n\%$ , the result for the original population lies between $\left(x-n\right)\%$ and $\left(x+n\right)\%$ .

A proposition on a voting ballot needs two thirds of votes to pass.

  $\begin{array}{c}\frac{2}{3}=\frac{2}{3}\times 100\%\\ =66.67\%\end{array}$

Therefore, the proposition on a voting ballot needs $66.67\%$ votes to pass.

A survey of a random sample of voters finds that $69\%$ of voters plan to vote for the proposition. The survey’s margin of error is $\pm 3\%$ .

Therefore, in original population the percentage of vote for the proposition lies between $\left(69-3\right)\%=66\%$ and $\left(69+3\right)\%=72\%$ .

Since, lower range of the vote percentage $\left(66\%\right)$ is lower than the required percentage $\left(66.67\%\right)$ , it cannot be conclude that the proposition will pass.