Question

A confidence interval for a population mean has a margin of error of $0.047$

a. Determine the length of the confidence interval.

b. If the sample mean is $0.205$, obtain the confidence interval.

c. Construct a graph that illustrates your results.

Short answer

a. The length of the confidence interval is $0.094$.

b. The confidence interval is $(0.158,0.252)$.

c.

Step-by-step solution

Given Information

It is given that confidence interval for a population mean has a margin of error of $0.047$.

Sample mean is$0.205$.

a. Determination of length of confidence

Margin error $E=0.047$

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

$=2\times 0.047$

$=0.094$

Hence, length of confidence is$0.094$.

b. Determination of confidence interval

Sample Mean $=0.205$

Confidence interval = Point estimate+ Margin of error

$=0.205\pm 0.047$

$=0.205-0.047,0.205+0.047$

$=0.158,0.252$

Hence, the confidence interval is$(0.158,0.252)$.

c. Graph of Confidence Interval

The graph is as below: