Question

use the confidence interval to find the margin of error and the sample mean. (0.396,0.620) the margin of error is 0.112. the sample mean is □.

Explanation:

Step1: Recall the formula for confidence interval

The confidence interval is given by \(\bar{x}-E\) (lower bound) and \(\bar{x} + E\) (upper bound), where \(\bar{x}\) is the sample mean and \(E\) is the margin of error. Also, \(\bar{x}=\frac{(\text{lower bound}+\text{upper bound})}{2}\).

Step2: Calculate the sample mean

Given lower bound \(L = 0.396\) and upper bound \(U=0.620\).

$$ \bar{x}=\frac{0.396 + 0.620}{2}=\frac{1.016}{2}=0.508 $$

Answer:

The sample mean is \(0.508\)