Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 8.2, Problem 23E
Automatic identification of the boundaries of significant structures within a medical image is an area of ongoing research. The paper “Automatic Segmentation of Medical Images Using Image Registration: Diagnostic and Simulation Applications” (J. of Medical Engr. and Tech., 2005: 53–63) discussed a new technique for such identification. A measure of the accuracy of the automatic region is the average linear displacement (ALD). The paper gave the following ALD observations for a sample of 49 kidneys (units of pixel dimensions).
- a. Summarize/describe the data.
- b. Is it plausible that ALD is at least approximately
normally distributed ? Must normality be assumed prior to calculating a CI for true average ALD or testing hypotheses about true average ALD? Explain. - c. The authors commented that in most cases the ALD is better than or of the order of 1.0. Does the data in fact provide strong evidence for concluding that true average ALD under these circumstances is less than 1.0? Carry out an appropriate test of hypotheses.
- d. Calculate an upper confidence bound for true average ALD using a confidence level of 95%, and interpret this bound.
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Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below.
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Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 10% level of significance.
(a) What is the level of significance?
(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)
SSTOT
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SSBET
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SSW
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Find d.f.BET, d.f.W, MSBET, and…
Chapter 8 Solutions
Probability and Statistics for Engineering and the Sciences
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