Chapter 11.5, Problem 4E

To determine

To find out: whether you can predict the winner among candidate A or candidate B.

Answer to Problem 4E

No, the winner cannot be predicted.

Explanation of Solution

Given information: Consider the question given to predict the winner among candidate A and candidate B when in a survey of $200$ voters with a margin of error of $\pm 7\%$ , $88$ voters plan to vote for candidate A while $112$ plan to vote for candidate B.

Calculation:

To find out whether you can predict the winner or not, follow the steps given below,

Find the percent of voters planning to vote-

Candidate A:

  $\frac{88}{200}=0.44=44\%$

Percentage of voters planning to vote candidate A is $44\%$ .

Candidate B:

  $\frac{112}{200}=0.56=56\%$

Percentage of voters planning to vote candidate B is $56\%$ .

Find the intervals in which each candidate’s percent of votes is most likely to lie with the help of margin of error.

  $\begin{array}{l}\text{Candidate A: }44\%-7\%=37\%44\%+7\%=51\%\\ \text{Candidate B: }56\%-7\%=49\%56\%+7\%=63\%\end{array}$

Hence, interval for candidate A is $37\%-51\%$ and for candidate B is $49\%-63\%$ .

The survey does not tell the winner of the election because the intervals overlap for the two candidates.