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Chapter 8: Q 8.49 (page 331)

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.

Short Answer

Expert verified

a. Length of confidence is 3.4.

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

c. The graph is:

Step by step solution

01

Given Information

Margin of error is 3.4.

Sample Mean is(49,4,56.2).

02

a. Determination of Length of Confidence

Margin Error E=3.4

Length of confidence is given as L=2E

L=2脳3.4

L=6.8

03

b. Determination of Confidence Interval

Sample Mean =52.8

Confidence Interval = Post Estimate 卤Margin of Error

=52.8卤3.4

=(52.8-3.4,52.8+3.4)

=(49.4,56.2)

Confidence Interval is(49.4,56.2)

04

Graph of Confidence Interval

The graph is shown below:

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Most popular questions from this chapter

The Coruro's Burrow. The subterranean coruro (Spalacopus cyanus) is a social rodent that lives in large colonies in underground burrows that can reach lengths of up to 600meters. Zoologists S. Begall and M. Gallardo studied the characteristics of the burrow systems of the subterranean coruro in central Chile and published their findings in the paper "Spalacopus cyanus (Rodentia: Octodontidac): An Extremist in Tunnel Constructing and Food Storing among Subterranean Mammals" (Journal of Zoology, Vol. 251. pp. 53-60). A sample of 51 burrows had the depths, in centimeters (cm), presented on the Weiss Stats site. Use the technology of your choice to do the following.

a. Obtain a normal probability plot. boxplot, histogram, and stem and leaf diagram of the data.

b. Based on your results from part (a), can you reasonably apply the t-interval procedure to the data? Explain your reasoning.

c. Find and interpret a 90%confidence interval for the mean depth of all subterranean coruro burrows.

Explain the effect on the margin of error and hence the effect on the accuracy of estimating a population mean by a sample mean.

Increasing the sample size while keeping the same confidence level.

Express the form of most of the confidence intervals that you will encounter in your study of statistics in terms of "point estimate" and "margin of error."

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.

Explain the effect on the margin of error and hence the effect on the accuracy of estimating a population mean by a sample mean.

Decreasing the confidence level while keeping the same sample size.
See all solutions

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