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Chapter 8: Q 8.50 (page 331)

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

Expert verified

a. The length of the confidence interval is 0.094.

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

c.

Step by step solution

01

Given Information

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

Sample mean is0.205.

02

a. Determination of length of confidence

Margin error E=0.047

Length of confidence is calculated as L=2E

=2×0.047

=0.094

Hence, length of confidence is0.094.

03

b. Determination of confidence interval

Sample Mean =0.205

Confidence interval = Point estimate+ Margin of error

=0.205±0.047

=0.205-0.047,0.205+0.047

=0.158,0.252

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

04

c. Graph of Confidence Interval

The graph is as below:

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