Question

A Census Burcau report on the income of Americans says that with 95% confidence themedian income of all U.S. households is $49,841 to $50,625. The point estimate and margin oferror for this interval are: *Point estimate = $49,841; Margin of error = $784Point estimate = $50,233; Margin of error = $784oPoint estimate = $50,233; Margin of error = $392Point estimate = $50,625; Margin of error = $392

Answer 1

Let the point estimate be x and the margin of error be e.

Then, we must have

`\begin{gathered} x+e=50625----------------------(1) \\ x-e=49841----------------------(2_{}) \end{gathered}`

Add the equation (1) and equation(2) to eliminate the variable e, we have

`\begin{gathered} 2x=100466 \\ \text{ thus} \\ x=(100466)/(2)=\text{ \$}50233 \end{gathered}`

Subtracting equation (2) from equation(1) to eliminate the variable x, we have

`\begin{gathered} 2e=784 \\ \text{ thus} \\ e=(784)/(2)=392 \end{gathered}`

Hence, the point estimate is $50233 and the margin of error is $392, The Third option