Question

A confidence interval for a population mean has a margin of error of $3.4$

a. Determine the length of the confidence interval.

b. If the sample mean is $52.8$, obtain the confidence interval.

c. Construct a graph that illustrates your results.

Short answer

a. Length of confidence is $3.4$.

b. Confidence interval is$(49,4,56.2)$.

c. The graph is:

Step-by-step solution

Given Information

Margin of error is $3.4$.

Sample Mean is$(49,4,56.2)$.

a. Determination of Length of Confidence

Margin Error $E=3.4$

Length of confidence is given as $L=2E$

$L=2\times 3.4$

$L=6.8$

b. Determination of Confidence Interval

Sample Mean $=52.8$

Confidence Interval = Post Estimate $\pm$Margin of Error

$=52.8\pm 3.4$

$=(52.8-3.4,52.8+3.4)$

$=(49.4,56.2)$

Confidence Interval is$(49.4,56.2)$

Graph of Confidence Interval

The graph is shown below: