ST 314 HW 1 - 15 points Due Wednesday, 1-16-12, at 2:00pm :

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Schutfort


Class Numbers:

________________________



ST 314 HW 1
-

15 points

Due
Wednesday,
1
-
1
6
-
12, at
2:00pm

:

You may work individually

or in groups of 2


3 people (submit
one assignment per group).
All work except for must be submitted on this sheet except when specified.


1. A study was done of the strength of high
-
performance concrete obtained by using superplastiziers
and certain binders. In particular, the following data was
gathered

on the flexural strength (a measure
of the ability to
resist

failure in bending), whic
h are measured in megapascals (MPa), for a sample of 2
8

beams made of high
-
performance concrete
.


5.9

7.2

7.3

6.3

8.1

6.8

7.0

7.6

6.8

6.4

8.3

6.3

7.9

9.0

8.2

8.7

7.8

9.7

8.5


7.7

9.7

7.8

7.7

11.6

10.3

11.8

10.7

13.1


a) Construct a stem
-
leaf display for
these data by hand. Include the number and depth columns on the
display.


















b) Discuss the distribution of the flexural strength of these beams made of high
-
performance concrete.
(ie symmetric, skewed, unimodal, outliers etc..)








c) Suppose that specifications state that the flexural strength of a beam must be 6.5 MPa or higher if it is
to be used as a support beam on a bridge. What proportion of the beams would meet specifications?





d) What do you think about the advisability

of using these beams as bridge supports?

Schutfort


Class Numbers:

________________________



2.

The following data are lifetimes (in hundreds of hours) of twenty
-
six 40
-
watt 110
-
volt internally
frosted incandescent lamps taken from forced life tests.


4
.
1

8.6

9.1

9.2

9.2

9.3

9.4

9.5

9.
5

9.6

9.7

9.
7

9.
8

9.9

10.4

10.5

10.6

10.7

10.9

10.9

11.0

11.3

11.6

11.7

12.4

13.4


a) Find the following


First Quartile ____________


Median ______________

Third Quartile __________


The step ___________


The lower fences
: inner _________


outer ____________


The
upper fences: inner _________


outer ____________


b) Construct a boxplot by hand below and label the axis






















c) Describe in words the distribution of the lifetimes of these 40
-
watt incandescent lamps.



Schutfort


Class Numbers:

________________________



3. An independent consumer group tested radial tires from two major brands to determine whether
there were any differences in the expected tread life. The resulting
data are in the file tire.txt.

a)
Construct stem
-
leaf displays (by hand sketch a back
-
to
-
back stem lea
f

display)



b)
Construct Parallel boxplots

(use Statgraphics)


c
)

Construct histograms

(use Statgraphics)


d
)

Comment on your results. What are the advantages and disadvantages of each display.
Discuss any
interesting features.

Does
one brand of tire appear to be superior to the other? Explain.