Question

use the confidence interval to find the margin of error and the sample mean. (0.104,0.260) the margin of error is the sample mean is

Explanation:

Step1: Find the sample mean

The sample mean $\bar{x}$ is the mid - point of the confidence interval. The formula for the mid - point of an interval $(a,b)$ is $\bar{x}=\frac{a + b}{2}$.
Here, $a = 0.104$ and $b=0.260$. So, $\bar{x}=\frac{0.104 + 0.260}{2}=\frac{0.364}{2}=0.182$.

Step2: Find the margin of error

The margin of error $E$ is given by $E=\frac{b - a}{2}$.
Substitute $a = 0.104$ and $b = 0.260$ into the formula: $E=\frac{0.260-0.104}{2}=\frac{0.156}{2}=0.078$.

Answer:

The margin of error is $0.078$.
The sample mean is $0.182$.