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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1.38 0.44 1.09 0.75 0.66 1.28 0.51 0.39 0.70 0.46 0.54 0.83 0.58 0.64 1.30 057 0.43 0.62 1.00 1.05 0.82 1.10 0.65 0.99 0.56 0.56 0.64 045 0.82 1.06 0.41 0.58 0.66 0.54 0.83 0.59 0.5 1.04 0.85 0.45 0.52 0.58 11 0.34 1.25 0.38 1.44 1.28 0.51