Question

Given the following confidence interval for a population mean compute the margin of error E

Answer 1

Given that the Confidence Interval for a population mean:

`11.81<\mu<13.21`

In this case, you can set up these two equations:

`\bar{x}+E=13.21\text{ \lparen Equation 1\rparen}`

`\bar{x}-E=11.81\text{ \lparen Equation 2\rparen}`

Because by definition:

`\bar{x}-E<\mu<\bar{x}+E`

Where "ME" is the margin of error and this is the mean:

`\bar{x}`

In this case, in order to find the "ME", you need to follow these steps:

1. Add Equation 1 and Equation 2:

`\begin{gathered} \bar{x}+E=13.21 \\ \bar{x}-E=11.81 \\ -------- \\ 2\bar{x}=25.02 \end{gathered}`

2. Solve for the mean:

`\begin{gathered} \bar{x}=(25.02)/(2) \\ \\ \bar{x}=12.51 \end{gathered}`

3. Substitute the mean into Equation 1 and solve for "ME":

`12.51+E=13.21`
`\begin{gathered} E=13.21-12.51 \\ E=0.7 \end{gathered}`

Hence, the answer is:

`E=0.7`