Question

use the confidence interval to find the margin of error and the sample mean. (0.214,0.350)
the margin of error is

Explanation:

Step1: Recall the formula for margin of error and sample - mean

The confidence interval is given by $(\bar{x}-E,\bar{x} + E)$, where $\bar{x}$ is the sample mean and $E$ is the margin of error. The mid - point of the confidence interval is the sample mean, and the margin of error is the distance from the sample mean to either end - point of the interval.

Step2: Calculate the sample mean

The sample mean $\bar{x}=\frac{0.214 + 0.350}{2}=\frac{0.564}{2}=0.282$.

Step3: Calculate the margin of error

The margin of error $E=\bar{x}-0.214$ (or $0.350-\bar{x}$). Substituting $\bar{x} = 0.282$, we get $E=0.282 - 0.214=0.068$.

Answer:

The margin of error is $0.068$ and the sample mean is $0.282$.