Annals of Biomed. Engr., 2005: 878–887 gave the follow- ing data on aortic root diameter cm and gender for a sam-
ple of patients having various degrees of aortic stenosis: M: 3.7 3.4 3.7 4.0 3.9 3.8 3.4 3.6 3.1 4.0 3.4 3.8 3.5
F: 3.8 2.6 3.2 3.0 4.3 3.5 3.1 3.1 3.2 3.0
a.
Compare and contrast the diameter observations for the two genders.
b.
Calculate a 10 trimmed mean for each of the two sam- ples, and compare to other measures of center for the
male sample, the interpolation method mentioned in Section 1.3 must be used.
68. a.
For what value of c is the quantity mini-
mized? [Hint: Take the derivative with respect to c, set equal to 0, and solve.]
b.
Using the result of part a, which of the two quantities and
will be smaller than the other assuming that
?
69. a.
Let a and b be constants and let for
. What are the relationships between and and
between and ?
b.
A sample of temperatures for initiating a certain chemi- cal reaction yielded a sample average °C of 87.3 and a
sample standard deviation of 1.04. What are the sample average and standard deviation measured in °F? [Hint:
. ]
70.
Elevated energy consumption during exercise continues after the workout ends. Because calories burned after exer-
cise contribute to weight loss and have other consequences, it is important to understand this process. The paper “Effect
of Weight Training Exercise and Treadmill Exercise on Post-Exercise Oxygen Consumption” Medicine and
Science in Sports and Exercise,
1998: 518–522 reported the accompanying data from a study in which oxygen con-
sumption liters was measured continuously for 30 minutes for each of 15 subjects both after a weight training exercise
and after a treadmill exercise.
Subject 1
2 3
4 5
6 7
Weight x
14.6 14.4 19.5 24.3 16.3 22.1 23.0 Treadmill
y 11.3 5.3 9.1 15.2 10.1 19.6 20.8 Subject
8 9
10 11
12 13
14 15
Weight x
18.7 19.0 17.0 19.1 19.6 23.2 18.5 15.9 Treadmill
y 10.3 10.3 2.6 16.6 22.4 23.6 12.6 4.4
a.
Construct a comparative boxplot of the weight and tread- mill observations, and comment on what you see.
b.
Because the data is in the form of x, y pairs, with x and y
measurements on the same variable under two different conditions, it is natural to focus on the differences within
pairs: . Construct a
boxplot of the sample differences. What does it suggest?
71.
Here is a description from Minitab of the strength data given in Exercise 13.
d
1
5 x
1
2 y
1
, c
, d
n
5 x
n
2 y
n
F 5
9 5
C 1 32
s
y 2
s
x 2
y x
i 5 1, 2,
c , n
y
i
5 ax
i
1 b x 2 m
gx
i
2 m
2
gx
i
2 x
2
gx
i
2 c
2
Variable N
Mean Median TrMean StDev SE Mean strength 153 135.39 135.40 135.41
4.59 0.37
Variable Minimum
Maximum Q1
Q3 strength
122.20 147.70
132.95 138.25
a.
Comment on any interesting features the quartiles and fourths are virtually identical here.
b.
Construct a boxplot of the data based on the quartiles, and comment on what you see.
72.
Anxiety disorders and symptoms can often be effectively treated with benzodiazepine medications. It is known that
animals exposed to stress exhibit a decrease in benzodi- azepine receptor binding in the frontal cortex. The paper
“Decreased Benzodiazepine Receptor Binding in Prefrontal Cortex in Combat-Related Posttraumatic Stress Disorder”
Amer. J. of Psychiatry, 2000: 1120–1126 described the first study of benzodiazepine receptor binding in individuals
suffering from PTSD. The accompanying data on a receptor binding measure adjusted distribution volume was read
from a graph in the paper.
PTSD: 10, 20, 25, 28, 31, 35, 37, 38, 38, 39, 39,
42, 46 Healthy:
23, 39, 40, 41, 43, 47, 51, 58, 63, 66, 67, 69, 72
Use various methods from this chapter to describe and sum- marize the data.
73.
The article “Can We Really Walk Straight?” Amer. J. of Physical Anthropology,
1992: 19–27 reported on an exper- iment in which each of 20 healthy men was asked to walk
as straight as possible to a target 60 m away at normal speed. Consider the following observations on cadence
number of strides per second:
.95 .85 .92 .95 .93
.86 1.00 .92 .85 .81 .78 .93 .93 1.05 .93 1.06 1.06 .96 .81 .96
Use the methods developed in this chapter to summarize the data; include an interpretation or discussion wherever
appropriate. [Note: The author of the article used a rather sophisticated statistical analysis to conclude that people
cannot walk in a straight line and suggested several expla- nations for this.]
74. The mode of a numerical data set is the value that occurs
most frequently in the set. a.
Determine the mode for the cadence data given in Exercise 73.
b.
For a categorical sample, how would you define the modal category?
75.
Specimens of three different types of rope wire were selected, and the fatigue limit MPa was determined for
each specimen, resulting in the accompanying data.
Type 1 350 350 350 358 370 370 370 371
371 372 372 384 391 391 392 Type 2
350 354 359 363 365 368 369 371 373 374 376 380 383 388 392
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Type 3 350 361 362 364 364 365 366 371
377 377 377 379 380 380 392
a.
