Question

Your friend decided to run for the President She tells you that in a pre-election poll the confidence interval for the proportion of people who would vote for her in the real election was 75% to 85%. What was point estimate? What was the margin of error for this confidence interval?

Answer 1

- The formula fo confidence interval is:

`\begin{gathered} CI=\bar{x}\pm ME \\ where, \\ \bar{x}=\text{ point estimate} \\ ME=\text{ Margin of error} \end{gathered}`

- Thus, we can apply the formula as follows:

`\begin{gathered} CI=\bar{x}-ME\text{ to }\bar{x}+ME \\ \\ \bar{x}-ME=75\% \\ \bar{x}+ME=85\% \\ \\ \text{ Add both equations to eliminate ME and find }\bar{x} \\ 2\bar{x}=(85+75)\% \\ 2\bar{x}=160\% \\ \text{ Divide both sides by 2} \\ \bar{x}=(160\%)/(2)=80\% \\ \\ \text{ Substituting the value of }\bar{x}\text{ into any of the equations,} \\ \bar{x}-ME=75\% \\ 80\%-ME=75\% \\ \text{ Make ME the subject of the formula,} \\ \\ ME=80\%-75\% \\ ME=5\% \end{gathered}`

Final Answer

`\begin{gathered} \text{ The point estimate is }80\% \\ \text{ } \\ \text{ The margin of error is }5\% \end{gathered}`