Q 8.49 - Elementary Statistics

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.

Step-by-Step Solution

Answer

a. Length of confidence is $3.4$.

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

c. The graph is:

Step 1: Given Information

Margin of error is $3.4$.

Sample Mean is $(49,4,56.2)$.

Step 2: a. Determination of Length of Confidence

Margin Error $E=3.4$

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

$L=2\times 3.4$

$L=6.8$

Step 3: 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 $(49.4,56.2)$

Step 4: Graph of Confidence Interval

The graph is shown below: