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StatisticsProbability and Statistics for Engineering and the SciencesAutomatic 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*arrow_forward*

9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

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).

**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.

Expert Solution

**a.**

To determine

Summarize the data.

**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.

Probability and Statistics for Engineering and the Sciences

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