Question

use the confidence interval to find the margin of error and the sample mean. (1.55,1.93) the margin of error is
(round to two decimal places as needed.) the sample mean is
(type an integer or a decimal.)

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, $a = 1.56$ and $b=1.93$. So, $\bar{x}=\frac{1.56 + 1.93}{2}=\frac{3.49}{2}=1.745$.

Step2: Calculate the margin of error

The margin of error $E$ is given by $E=\frac{b - a}{2}$.
Substitute $a = 1.56$ and $b = 1.93$ into the formula: $E=\frac{1.93-1.56}{2}=\frac{0.37}{2}=0.185\approx0.19$.

Answer:

The margin of error is $0.19$.
The sample mean is $1.745$.