Q 8.52 - Elementary Statistics

Question

A confidence interval for a population mean has a length of $162.6$.

a. Determine the margin of error.

b. If the sample mean is $643.1$, determine the confidence interval.

c. Construct a graph that illustrates your results.

Step-by-Step Solution

Answer

a. The margin of error is $81.3$

b. The confidence interval is $(561.8,724.4)$.

c. 

Step 1: Given Information

It is given that length of confidence interval is $162.6$ and sample mean is $643.1$

Step 2: a. Determination of Margin of Error

Length of confidence interval is $L=162.6$

Margin of Error is half the length of confidence interval.

Margin of Error $=\frac{1}{2}\times 162.6$

Margin of Error $=81.3$

Step 2: b. Determination of Confidence Interval

Confidence Interval = Point estimate $\pm$ Margin of error

$=643.1\pm 81.3$

$=(643.1-81.3,643.1+81.3)$

Required Confidence Interval is $(561.8,724.4)$.

Step 3: Graph

Required Graph is