Question

use the given confidence interval to find the margin of error and the sample mean. (6.37,11.21) 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, $a = 6.37$ and $b=11.21$. So, $\bar{x}=\frac{6.37+11.21}{2}$.
First, add the two numbers: $6.37+11.21 = 17.58$.
Then, divide by 2: $\frac{17.58}{2}=8.79$.

Step2: Calculate the margin of error

The margin of error $E$ can be found using the formula $E=\frac{b - a}{2}$.
Substitute $a = 6.37$ and $b = 11.21$ into the formula: $E=\frac{11.21-6.37}{2}$.
First, subtract: $11.21 - 6.37=4.84$.
Then, divide by 2: $\frac{4.84}{2}=2.42$.

Answer:

The sample mean is $8.79$ and the margin of error is $2.42$.