Question

use the confidence interval to find the margin of error and the sample mean. (0.204, 0.320) the margin of error is
the sample mean is

Explanation:

Step1: Calculate 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, $a = 0.204$ and $b=0.320$. So, $\bar{x}=\frac{0.204+0.320}{2}=\frac{0.524}{2}=0.262$.

Step2: Calculate the margin of error

The margin of error $E$ is given by $E=\frac{b - a}{2}$.
Substitute $a = 0.204$ and $b = 0.320$ into the formula: $E=\frac{0.320 - 0.204}{2}=\frac{0.116}{2}=0.058$.

Answer:

The margin of error is $0.058$.
The sample mean is $0.262$.