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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.

BuyFind

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809
BuyFind

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

Solutions

Chapter
Section
Chapter 8.2, Problem 23E
Textbook Problem

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).

  1. a. Summarize/describe the data.
  2. 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.
  3. 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.
  4. d. Calculate an upper confidence bound for true average ALD using a confidence level of 95%, and interpret this bound.

Expert Solution

a.

To determine

Summarize the data.

Explanation of Solution

Given info:

The measurements of the accuracy of automatic region of 49 kidneys are given.

Calculation:

Software procedure:

Step by step procedure to obtain the descriptive statistics using the MINITAB software:

  • Choose Stat > Basic Statistics > Display Descriptive Statistics.
  • In Variables enter the columns ALD.
  • Click OK.

Output using the MINITAB software is given below:

Expert Solution

b.

To determine

Explain whether ALD is at least approximately normally distributed or not.

Explain whether it is must to assume normality for finding the confidence interval.

Expert Solution

c.

To determine

Test whether the true average ALD under these circumstances is less than 1.

Expert Solution

d.

To determine

Find the upper confidence bound for the true average ALD using a confidence level of 95%.

Interpret the bound.

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Chapter 8 Solutions

Probability and Statistics for Engineering and the Sciences
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