Q 8.51 - Elementary Statistics

Question

A confidence interval for a population mean has length $20$ .

a. Determine the margin of error.

b. If the sample mean is $60$ , obtain the confidence interval.

c. Construct a graph that illustrates your results.

Step-by-Step Solution

Answer

a. Margin of error is $10$.

b. Confidence interval length is $\left(50,70\right)$.

c. 

Step 1: Given Information

It is given that Length of confidence interval is $20$ and sample mean is $60$.

Step 2: a. Determination of Margin of Error.

Length of population mean $L=20$

Margin of Error$=\frac{1}{2}\times 20$

Margin of Error $=10$

Step 3: b. Determination of Confidence Interval

Confidence interval = Point estimate + Margin of error

$=60\pm 10$

$=(60-10,60+10)$

$=(50,70)$

Step 4: c. Graph

The graph is as below: