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Chapter 8: Q 8.7RP. (page 346)
A confidence interval for a population mean has a margin of error of
a. Obtain the length of the confidence interval.
b. If the mean of the sample is , determine the confidence interval.
Part (a)
Part (b)
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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 meters. 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. ). A sample of 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 interval procedure to the data? Explain your reasoning.
c. Find and interpret a 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.
Decreasing the confidence level while keeping the same sample size.
State True or False. Give Reasons for your answers.
The confidence interval can be obtained if you know only the margin of error and the sample mean.
Suppose that a simple random sample is taken from a normal population having a standard deviation of for the purpose of obtaining a confidence interval for the mean of the population.
a. If the sample size is , obtain the margin of error.
b. Repeat part (a) for a sample size of
c. Can you guess the margin of error for a sample size of ? Explain your reasoning.
What is a confidence interval estimate of a parameter? Why is such an estimate superior to a point estimate?
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