Q 8.50 - Elementary Statistics

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.

Step-by-Step Solution

Answer

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

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

c. 

Step 1: Given Information

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

Sample mean is $0.205$.

Step 2: 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 $0.094$.

Step 3: 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 $(0.158,0.252)$.

Step 4: c. Graph of Confidence Interval

The graph is as below: