34 bootstrap confidence intervals using percentiles

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Finite Mathematics and Applied Calculus
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Chapter 9 / Exercise 70
Finite Mathematics and Applied Calculus
Costenoble/Waner
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3.4 : Bootstrap Confidence Intervals using PercentilesIn the previous sections we looked at how to construct a 95% confidence interval, where we estimated the SE by using the sampling distribution or the bootstrap distribution. In this section we are going to look at how to create a confidence interval for any level of confidence using a bootstrap distribution.
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Finite Mathematics and Applied Calculus
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Chapter 9 / Exercise 70
Finite Mathematics and Applied Calculus
Costenoble/Waner
Expert Verified
.
Example: Body Temperature Is normal body temperature really 98.6 ◦F? A sample of body temperature for 50 healthy individuals was taken. Find this dataset in StatKey under “Confidence Interval for a Mean” or as BodyFat50 in the text’s datasets.(a)What is the sample mean? What is the sample standard deviation?
(b) Generate a bootstrap distribution, using at least 1000 simulated statistics. What is the standard error?
(c)Use the standard error to find a 95% confidence interval. Show your work. Is 98.6 in the
(d) Using the same distribution, find a 95% confidence interval using the “Two-tail” option on StatKey (or other technology to give percentiles from the bootstrap distribution).
(e) Compare the two 95% confidence intervals you found. Are they similar?
(f) Still using the same bootstrap distribution, give a 99% confidence interval.
(g) Is the 99% confidence interval wider or narrower than the 95% confidence interval?
(h) Clearly interpret the 99% confidence interval We are 99% sure that the mean body temperature for all healthy individuals is between98.017 and 98.544.Example: Problems with Bootstrap Distributions If a bootstrap distribution is not relatively symmetric, it is not appropriate to use the methods of this chapter to construct a confidence interval. Consider the following data set: 5, 6, 7, 8, 25, 100 (a) What is the standard deviation of this dataset?
(b) Use StatKey (or other technology) to create a bootstrap distribution for the standard deviationof this dataset. Describe the distribution. Is the distribution symmetric and bell-shaped?
(c) Is it appropriate to use the methods of this section to find a bootstrap confidence interval for this standard deviation?
(d) Discuss with a neighbor why the bootstrap distribution might look the way it does.

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