Chapter 9.3, Problem 9.44E

To determine

To find the 95% confidence interval for p

Answer to Problem 9.44E

The 95% confidence interval is, (49%,55%)

Explanation of Solution

Given:

C=confidence level = 0.95

Sample proportion:

  $\widehat{p}=52\%=0.52$

Margin of error = E = 3% = 0.03

Formula:

Confidence interval for population proportion is,

  $CI=\widehat{p}\mp E$

Calculation:

  $\begin{array}{l}\widehat{p}-E=0.52-0.03=0.49=49\%\\ \widehat{p}+E=0.52+0.03=0.55=55\%\end{array}$

The election is too close to call, because 50% is within the confidence interval and 50% corresponds with a tie for two candidates.