SUMMARY
COVERSHEET
Tntroduction of the Conputer in the Statistics
Subnitted to the office of ConDutinq Activities
Title:
ProsT'am
')
]
f6r
Dew.l^nird
a^m.,'F-;
l!.^.
Nane of lnstitution
HoDe Coll,eee
Address:
State
City
Holland
Grant to:
Curriculunr
Under the
Zip Code qg423
Michigan
Hope Collese
be made)
3.
Clarence Handlogten, Treasurer-and Business Manaser
(Nane ano
taile
or
Elliot A. Tanis
Directora's na&e
Telephone:
$!ea
5.
616
cnle!
admlnlsl-rat.Lve
urrace
Period covered in this
No.
TotaL amount requested
anst-tution)
Mathernatics
Depar-tnent
392-5111
296-8384
ljeDt. No.
Home Phone
proDosal: June, 197L to Ausust. 1973
brarllng
7.
of
481-34-8023
Socaal Security No.
Ext.2266
uooe
otticer
fron
the National
oate
Enqt_ng t ate
Sc i e n c e
a. /fo--,,)
Clarence Handlogten, Treasqrer t Business Mana
liame and ri!:e
of or-iiciai--EItEoFf2EE--Eer
to sign for institution
PRoP0SAL: lNTRoDUCTI0NOT THE COI4PUTER
]N THE STATISTICS CURR]CULUM
Elliot A. Tanis
Herbelt L. Dershen
Hope College
Holland, Michigan
S e p t e n b e r 1 , 1 9 70
,
The modenn digital
of statistics
to undergraduates.
courses introduced
of statistics
along five
l-.
conputer has greatly
enhanced the teaching
Many studies
have been nade and
which use the conputer as a tool
(see references).
Tbese efforts
in the teaching
have been diuected
general" lines.
Gener.ating empirical
data,
would spend nany hours throwing
Whereas previously
dice,
the cornputet" can pr.ovide a much larger
flipping
students
coins or drawing cards,
volume of data in a matter
of
geconds.
statisticaL
that
were only illustrated
DrinciDles.
by textbobk
3.
perforn
of the pninciple
ance or regression
bers and receive
interpreting
4,
this
The use of special
stati6ticaL
analysis)
the
purpose subr.outines to
procedure (such as analysis
gives the student
an analysis
of va:ri-
a chance to input
f!,on which he may gain experience
num-
in
results.
Stoning raw data.
amount of naw data collected
lray that
data and then testing
under study.
Stot?ed p!'ograms.
a conplicated
pr.inciples
examples can now be "discove!.edtl
by the student by gener"ating the enpi.rical
validity
Statistical
students
The conputer can be used to 6tore
ft orn real
and instructors
life
observations
can perforn
statistical
a lar"ge
in such a
analyses of
data.
5.
Conputer-assisted instiuction.
A systen which al1ows for
- 2 -
interaction
alfowing
bet\"reen the student
and the computeu can be utilized
the machine to tr-rtor the student,
step through the piocess of learning
i.e.,
to take him step by
the statistical_
Epending as nuch time at each step as the student
principles,
needs,
Each of these uses of the conputer in the stati.stics
great nerit lrhen enployed in the proper situation.
has
examine the effect
curriculun
of introducing
the conputer into
however, that
we wish to
ou1. statistics
the computer can senve as a more vaLuable
tooL when the student must do a Significant
hfurse1f.
If
a student
anount of the prograrming
is able to progran the correct
he inust have a nore than superfj.cial-
the pnoblen is
ations
culriculun
at Hope College in the above ways.
We feel,
problen,
by
that
soLved.
night
This proposal
He must take into
be encounter.ed and all
is nade with
i.nto the statistics
sofution
understanding
of a
of how
account al"l possible
possible
situ_
aets of input
the purpose of incorponating
this
data,
idea
cur.riculum at Hope College.
DESCRIPTIONOF PROPOSED
COURSES
The Hope College Mathenatics
course sequences in statistics:
depantment currently
Math 35, Introductory
and l,lath 55-56 Mathenatical" probability
to nodify
naterial
in an integnal
rationale
A+
&atics
these courses by introducing
fol-low for
l-ha
nnac6h+
way.
offers
tr^ro
Statistics
and Statistic6.
and
!.te propose
the conputer into
Our nethod fon doing this
the course
and the
the two Eequences considered separ.ate1y.
+L!!Lc
im6
rLrler.e
l
alte
t$ro
corlt ses
offered
department at Hope College which are either
r.ecomnendedfon najor:s in the fields
business adninistration,
sociology
courses are Mathematics 27, Introduction
the
nathe_
requined or strongl-y
of psychology,
aDd political
by
econonics and
science.
to Digital
These two
Computens and
- 3 1.
Mathe$atics
ter
35, Introductory
- hour coutse
in which
on the fBM U30 while
giving
a generaf
introduction
could
berefit
fron
cal analysis.
By learning
behind
their
ove!' the present
without
fron
their"
lelated
najon
could under,_
and gain practice
eltrlangenent whene progr.amning nust
For exanples
currentl-y
statisti_
the statiE-
This would be a signifieant
to Po?tran.
to statistics
with
the students
background for
each
ax.e motivated
ar.ea which nequine
the prognans they wlite
results.
that
a.two_
Computen pro_
when the students
irnpnovebe taught
the atudent
progr?ans assigned ar,e usuaLLy nothing
to be translated
is feft
of the other.
theee problens,
assuuing any statistieal
statisticaL
It
pnogramrning in conjunction
analyzing
the analysis
in i.ntenp:reting
nent
The catar-og descr:iption
these t!.ro one-semester courses into
more readiLy
probleo.s
necessary for
_ houll course
senester
to statistics.
the xoateriaL
by interesting
stand
is a three
se(Luence, tlDaee hours each se;ester.
gnanning.can be taught
tics
leax"n to prognam in Fortran
found in Appendix A.
I{e pnopose to con}ine
course
The formetr is a two senes_
the students
the latter
of these two courses is
senester
Statistics.
and hence
none than fonnulas
of the types
assigned in the llath
of prograna
2Z courise, see
Appendix B.
The above could
statiEtics
that
this
a p?erequisite
an argunent
their
be presented
combination
for
thei?
iatical.
as an optimal
But we also believa
approactr can also
soLution.
elenentary
be given
leaving
We agai.n emphasize that
f!'om most cunrently
established
computer-
courses inas!0uch as we would have students writing
own prognams rather
routines.
the prograruning.
the opposite
course would differ
aided statistics
for
as an angument fon naking
than depending
(We do not,
on previously
prepared
however, !ul-e out the use of such
stat-
- 4 1:
routines
in this
course where we feel
eornputen can be an effective
thoroughly
Perforn
understand
it.
pedagogical tool
a technique
This fact
they would be useful).
befole
he can i,mitd
cou.se6'
in such a way that
statistics.
but would invorve
the student
the latest
previously
will
require
will
necessani.ly be taught
of the naterial
enough pl"ogramming
learned can be illustnated
tearned statistics.
a Large amount of planning.
na1 practiee.
early
an intenveaving
of the
technique and knows enough stati.tics
plograrnjning principle
examples invoLving
a combinatj.on
a1way6 has leanned
to pnogr"en the next statistical
that
a progtram to
in nurnerical analysis,
The proposed cout?se would not be simply
two present
since the student nust
has been long utilized
but 6e1dom in connection with
The
by
This obviousfy
The prograrming
in a sequence which differ.s
Por exarpLe, subscr.ipted variablee
nateriaL
fton
the no!,_
!qil1 be intnoduced
in the course nathen than towand the end as is u6ua1 6ince
nost €tatietical
roing eoncepts will
applications
require
their
Length and the pnesent cour"ses totaL
of additional
with which social
lrhich
Seldon used progran_
be placed nean the end of the course,
Since the pnoposed cour.se is a total
introduction
use.
topics
and behavional
are not included
scientists
semester_hours i.n
there will
in statistics
in the current
are randon number generators,
f,ive,
of six
be tine
beginning
with
should be famiLiar
cunricuLum.
Monte Carlo techniques
ordera to drarv certain
divided
into
and nefining
conclusions
tedns of students
this
and simulation.
with sinilar
This grouLd
experiment or
data statistically
florn the data.
and
Sone. such topics
raw data firord a vrell-defined
obsenvation, and analyzing
the
and computer science
The students would also be expected to complete a ploject.
involve
for
The class
interests
in
would be
and each team
- 5 .,:
would attack
a problem related
The effectiveness
the quality
obtait
various
depaltnents
resealch
classroon
these with
articles
tg obtain
depend. substantially
these projects
on
as welr
exampl_esand homework assiqDnents.
fi:orn thei!
a collection
the class
the assistance
in their
A useful
in his
course wifl
l
We wilt
that
of this
of the problems and data used for
as pnobleng used for
lems.
to their" field.
own !"esearch arld fron
areas of inierest.
of interesting,
side effect
analyeis
of our colleagues
useful
fon the professor
night
provide
in the
te)<tbooks a4d
In this
way we hope
and non_ttrivial,
pnoviding
€one additional
prob_
the problen
i.nsight
is
fon him
own wonk .
MATHEMAT
ICAI. PROBABILITY AND STATISTICS
We teach a two semesten, three
Level mathematical
For this
course we believe
the theory
of probability
We fulther
This can often
Howeve!,
probabiLity
believe
and 6tati6tics
it
is
inpo:rtant
and Etatistical
that
be done vely
it
is
Einply
iunion_senion
courise (eee Appendix A),
fon the studenta
the Central
impontant to illustrate
with
Limit
sdnple from sever"aL distributionS,
way the
student
gets
dice,
the theory,
carde on a spinnen.
Theoren, it
is
using different
sone feeLing
to ]eann
infer"ence.
fon many exampLes the eonputer" i.s an invaluabfe
To iLlustr.ate
this
houns pen sene8ter,
for
the fact
aid.
j.nstructive
sarple
sizes.
to
In
that
o/^ln
has a l-inj.ting
this
N(0,1)
distribution.
an example of
i d e aFor Monte Ca?lo techniques
ben generator
ing
See Appendix C for
is necessaly.
trandom numbers tt, it
is
and sirulation,
a pseudo-nandom num_
Given a deterninistic
an inst!,uctive
exercise
nethod for generatfor. students to
- 6 -
test
statistical
find
the probability
generate
properties
density
functions
E.g.,
we can
of ordeu statistics.
Now
8000 sets of 4 lrandon numbers.. Order each set of
4 nunbers.
Do the 8000 snalLest
bution
of the numbers gener,ated.
numbers represent
of the snallest
a random sanpfe from the distri_
o?der statistic?
See Appendix C for
an expan_
sion of these ideas,
Confidence intervals
e. g. , . 9 0? confidence
If
intenvals .
Xr, Xr, ---,
distribution,
fon rneans can be simulated
See Appendix C ,
is a random sample of size n fnom a normal
X_
mean p, variance o2, tnenr!,
- pf /a2 has a chi_square
$i
y = n degrees of fr.eedon wnile-!-
distribution
nith
a chi-equare
distribution
to ill-ustrate.
with
y = n-l
(Xi _ X)r/o2
degrees of fr.eedon.
of one degnee of freedorn can be illustrated
has
This loss
thr.ough siruLation
on the
compute!",
fn order fon sinulation
Lustnate
the theory,
it
on the conputer to nost effectivefy
would be beneficial
for
each student
no6t of his own pnogra.rns. This woufd necessitate
a prer"equisite
available,
part
fon thi.s course.
e.g.
for
ordering
data or grouping data.
statistics
should be written
the rnost benefit
The fact
fron
that
this
this
the theory
by the student
to write
naking prograrnrning
Selected subroutines
of the program which iffustrates
il_
should be made
However, that
in probabifity
in orden that
and
he der.ive
experience.
procedure is effective
by 5 Hope College- students who did wnite
their
has been denonstrated
own prograrns for
undet _
graduate research proj ects,
In order that
there would be sufficient
of the necessary material,
each semester.
we desire
It
is
coLfse tine
to cover all
we propose to add a t$ro hour laboratoriy
in developing naterials
the support of NSF.
for. this
laboratory
that
-'l -
sets
Inadditiontoillust]ratingtheory'wewouldliketogatherdata
of live data in the san\e v/ay as ProPosed for the introd'jctory
course.
statistics
It
will
the ti'io
to ap-
can learn
way students
In this
cfasses to sharle the sa,ne data.
situations'
infenence in real-life
p1y statistical
in many cases for
be Possible
IN STATISTICS
PREVIOUSEXPERIENCLWITH COMPUTERS
into
Much Previous work has been done in introducing the conputer
curriculurn he!'e at Hope' Dr' 'tay E' Polkert was a
the statistics
.
Dr. lolkert
and statistics.
putels
conputet mainly
fustrate
of Nolth Carolina
in the University
participant
exPerimented with
in the fonn of Previously
the theory
NSI project
in the intx'oductory
on con-
the use of the
to i1-
PrePared subroutines
cour"se'
statistics
D!'
Het'bert
Det"shendidtheProgralmingandProvidedconsultationfor.thisProject'
Drr.EltiotTanishasusedthecornputerextensivelyinhisnathe.
counse and in undergraduate reand statistics
natical- probability
It is flon this exper(8ee APPendix D)'
search projects in statistics
and D:r' Tanis and the conience, the reco[uiendations of Dr' Io]'kert
nents of their
students
the proposed revisions
that
to ouL statistics
arise.
curriculum
PROPOSAL
We ProPose to acconplish
riculun
ing fron
the modifications
cur-
to the statistics
peLiod stretchPhase Program over a
This period includes
the Surrmenof l9?1 to the Sunner of 1s73'
at HoPe col-lege in a flve
twoacadenicyea'san.lwillthefeforeaffordtheoPportunitytoteach
both course sequences twice '
Phase I of the Project
this
.
period
will
of 1971'
occur in the Surnrner"
Dr. Tanis and Dr. Dershen slil1 nake Preparations
courses to be taught
the following
academic yeai'
This nill
During
for
the
involve
- 8 -
the planning
and arnnanging of natenial
introductory
statistic_s
neaningful
of useful
certain
routine€.
all
.dents,
sequence for
and pr.ognaruning couz,se, the development
expe:riments and useful
plloblens
in a logical
neal_life
and e)<amples for
data sets,
the cqlputer,
The two pr.ofessons lrill
be tnained
of
the design
and the vEiting
be assisted
by fou,
of whorni,riltr have taken one yeall of mathematical
These students will
the
to be lab agsistanb
of
stu_
statistics.
the folfowins
acadenic yean.
The second phase will
eonsist
first
of the teaching
tinre,
of the tto
and Etatistice
throughout
that
Du. Tanis wi1l
counse.
the year.
is anticipated
it
wilL
posed courae lequirenents.
pnevious summenwill
include
Each wilL
Students will
statistj.cs
teach the nathematical
consul-t with
assiBt
with
be no textbooks
The four
and
p!"oba_
the laboriatory.
It
notes in each
which folLow ouu p!.o_
students who were j.nvolved the
now serve as laboz,atory assistants.
assistance
the
the other
be necessary to dietribute
of these counses as there will
duti.es will
pr"opased course sequences for
Dr', Dershen vrilL teach the introductory
prograruning course while
bility
span the 1971_22 acadenic yeat and will
in the preparation
their
of notes,
naintaining
softwane developed in the pnevioue sun]Ilter, devefop new softwar"e as
.the need arises,
aasist
the conputer. for
the students.
fot
students
Drs, Dershem and Tanis for
in pnograrn debugging and operate
One quarter
the prepalation
In the Suruler of 1972, phase III
will
involve
for
of notes.
of the project
the developnent of new software,
expeniments and the holding
nelease time is p:roposed
of a conference.
the designing
deseription
nDissemination
of this
of Infornation'r.
in this
This
of new
This conference wilL
educators .from the Midwest who ane intenested
detailed
is planned.
program,
be
A
conference is found in the section
Tr,rostudents
who conpleted
the :naihe_
- 9 -
matical
probability
year will
and statistics
sequence in the 1971_72 acadenic
be employed as assistants
Phase IV wi1l
include
for phase III.
the acadenic yea? !g,12_j3 and consist
the second teaching
of both of the new courses.
be tr"ied,
o1d ineffective
pt'ojects
replacing
and experinents
rvilr
be attenpted.
ployed to assist
px,obabifity
Nevr approaches will
approaches and neii, exampl-es,
to the notes ppepared a year befor.e.
the new mathematical
of
Revisions r!'i11 be nade
Foun students who have completed
and statistics
as in the previous
year,,
sequence will
be em_
Two of these students will
have assisted in phase IIf.
The Sunner of f973 witf
entire
be the fifth
progt?d,ora'ill be evaluated
years.
Those experinents
to all
other interested
phase the
and recomnendations nade for
\"ii11 be accunulated
future
ancl our final
con_
and prepared for
nho attended the conference in phase III
and anv
educators -
.
DISSEMINATIONOF INFORMATION
In the sunler
the results
inpnovenent.
of f972 a conference eril1 be scheduled to report
of our first
Invited
of the nathenatics
yeat of study and to solicit
to this
departnents
confe!,ence will
of alf
at this
confenence to approxinately
is after
fifty
for
nembers
in the Mid_
the attendance
panticipants.
The confenence
adequate preparation
and so that
t h e c o m p f e t i o n o f m o s t s u n r n e rs e s s i o n s .
The confefence irill
begin on Monday with
folLorved by rnorning and afternoon
and a final
be interested
We r^ri1l limit
i.'i11 be scheduled in August to allow
suggestions
foun year colleges
west area who have conputer. facilities.
it
In this
judged the nost effective
cLu6ions r.egarding the pnoject
distribution
phase.
an afternoon
session,
sessions Tuesday through Thursday
session on Friday norning,
A1l sessions ,rill
be chaired
by Dl'. Tanis or Dr. Dershen.
lines
of the coulses
to the palticipants
as they stand at this
tine
problens
wi]]
and out_
be distributed
.
The foflor',ing
and sent to alt
Copies of interesting
suruner' an update of these nateriars
participants
of the confelence
will
be made
and to anyone else
v,ho has requestea LoTiaaea to our ma-iljng
list,
PIRSONNEL
The pr.incipal
Dershem.
Dr. Tanis will
nathematical
direct
personnel
will
be Dr,. Elliot
Tanis and Dr. Herber:t
irave the pnir[ary responsibilaty
probability
and statistics
cou.se while
A resuEe of these tiro pnofessors
Dr. Jay Folkent,
Hope College,
will
in introductory
course at Hope College
.
facitity
conplenent
of supporting
calcufator
center
currently
on compurers
the introductor"y
the computer for
is the IBM 1130.
equipnent
complete with
computations
available,
0f the six
able for
of North Canolina pnoject
statisti.cs
one year.
FACILITIES
The principal
snalle!
at
was a partici_
and taught
using
of mathenatics
Dr. polkert
senve as a consultant.
statistics
and progranuning
is found in Appendix E.
chairman of the departnent
pant in the NSF - University
the
Dr. Dershem lrill
the developrnent of the introdu qtory statistics
course.
for
easily,
for
Hope Coltege has a fult
the 1130 and an extensive
prognanmable calculators
For a complete listing
trdo ner^rcourses will
overtd<ed keypunches.
punches are included
of facilities
see Appendix t.
029 keypunches o!^rnedby the college,
Student use.
to handte
]t
is
greatfy
expected that
increase
the introduction
the demand for
Hence, funds fon renting
in the budget of this
four
are availof these
the$e aLready
two additional
proposal.
key_
- t l tt-
The computer center
will
be able to supply none than an adequate
amount of computation powen to handle the
needs of this project.
Educational programs of students and professors
have top priority
on
the nachine and turh around time for
student jobs is seldon none than
one hour at any time.
Many studentS find it mor.e convenient
to run
their programs in the evening.
The computet" center is cunrently kept
open in the evenings for this eole pur.pose.
One of the puuposes of
the student aseistants in this pt"oject is
to ar.low the tine available
for
.
student runs in the evening to be expanded
by having the assistants
openate the conputer for an additionalportion
of the evening hours
in onder to rnininize the inpact of these new
courses on the no!,nal
day-tine canputer echedule,
- 1 2 -
BUDGET
rnase l - suruten, lg71
Salaries I
1)
Etliot
2)
Herbert Detrshen, 2/9 of g1Z1600
2800.00
3)
4 student aesistants,
2880.00
Other dinect
' t[)
Tanis, 2/9 of $13,S00
$ 3 o o oo.o
t2 weeks @g60/wk
costs:
Keypunch rental,
3 nonthE @$69.30/nonth
5)
Refenence naterial
6)
Consulting
7)
Expendable equipnent and supplie6_2t
dLnect oPenating costs
Phase I direct
207.90
100.00
fees
s00.00
of other
cost6 - total
Phase fI
- Acadenic yea!,
19?1-?2
Salaries I
1)
E t t i o t T a n i s , l / q o f $ 1 3, S 0 0
2)
H e n b e r " tD e r e h e n , t / a o f $ 1 2 , 6 b 0
3)
4 student assistants, 5 hr./wk, $1.60/h!.
for 30 weeks
93375.00
3150.00
900.00
other direct cost8:
t+) Keypunchrental,
5)
2 for 9 nonthE @$69.30/nonth
Expendabl.eequipnent and supp].ies _ 2t of other
q].r'ect oPeratj.ng costs
Pha6e II
direct
coEts - total
rnase
Salaries
L74.00
$8846.40
-L_11-
Suruner, 1972
I
1)-2)
3)
1 2 4 ?. 4 0
Same as phase I
Two student assistanrs,
$5800,00
1 2 w e e k sG $ 6 0 . 0 0 / w k
1.440.00
- 1 3 !
Conference expen6ea:
-
.
4)
Travel expenses-fon conference panticipanl_<
@500Ei].ei /participant
@Bl/:nite.
"
ffiit.ffii.:;a,.d'
ot
ruDtaeaty
cn
4 davsror 50 participants
$2000.00
2000.00
200.00
other direct costs:
7)
Keypunch r.enta1,
8)
Expendable equipment and €upplies
qLrect operati.ng costs
Pha6e IIf
direct
2 fot, 3 nonthe @ S6 9.3 0/nonth
- 28 of othe?
costs - total
4 1 5 .8 0
2 3 7. 0 0
912092.80
Pha6e IV, Academic yea? L97Z-73
Salariee i
I)
.
4 student aesistants,
S hr/wk. for 30. i,rks
s 900.00
other d i r e c t c o s t s :
2)
Keypunch rental,
3)
Expendable equiplent and supplie8 - 2g of other
drr]ect operatLng costs
aane as q) phaee II
1247.40
$2r.90.40
Phaae V, Sumnren,1gZ3
Salaries:
L)
Elliot
2)
Herbert Dershen, 1/9 of 912,600
3)
Secretarial
Other direct
.4)
Tanis, t/9
of $1g,S0O
1400.00
500.00
costs i
Expendable equiproent and supplies
<rlrect operatang cost S
Phase V direct
$1s00.00
costs
- total
- 2? of other
68,00
$3458.00
budeet - All
Total
Total
1)
Salaries - sta Ff
2)
Salaries
3)
Keypunch rental
4)
Reference naterial
5)
Consulting fees
6)
Conference expenses
7)
Expendable equiprnent and supplies
8)
SecretariaL
direct
fndirect
Total
five
phases
$21,02s.00
- students
6,120,00
3,118.50
100.00
500.00
4,200.00
1 1 2, 0 0
500.00
costs
costs - 45.33 of l)
costs - dinect
9,524.32
and indirect
$45,799.82
Supplenental
SaLaries.
The salaries
on arstinations
.of funding.
of thein
Budget lnfornatian
of Dn. Tanis and Dn. Dershem are b a se d
average nine nonth salaniea
These arounts will
vary slightly
over the perl.od
from the actuaL ajn-
ounts budgeted, but they should be veny close to correct.
ConsuLting fees.
The consufting
:reinbur.se the nenbers of the social
vrho serve as consultants
data and problens
for
include
ter
supplies,
paper, duplicating
Indirect
the negotiated
costs.
be used to
science faculty
per.sonnel with
use in the proposed courses.
and supplies.
conputed at 2Z of all
conputer
and behavioral
by pr.ovidj.ng the project
Expendable equipnent
supplies,
fees budgeted !,rilf
The expendable equipnent
othe!, direct
such as printet"
suppties
fhe indirect
and
operating
forns,
IBM cards and plot-
and Etationerv,
costs vrere conputed in accord niith
agneenent dated Aprif
29, Ig70.
A xerox copy of this
- 1 5 '{
agreement is
contained
Computqr tine.
in Appendix H.
The charge fon use of the Hope College
IBM
f1g0 i6 $30.00 pe'" hour.
A11 conputer charges nelated to this
project lrill_ be a contribution
to the pnoject by Hope ColLege. It
is eEtimated that this project !rit1
require over $9,000 worth of
conputeri tine.
)
APPEND]X A
CATALOGDESCRIPTIONOT CURRENT
COURSES
l,lathematics 27.
bifities
of digital
languages liith
emphasis on FoRTMN.
tions
with
3S.
Introductory
Includes
random vaniables,
55.
experience with
a
in the studentrs
_ A general
introduc_
students majoning in otherl
and no!,naf distribu_
and testing
56.
probability
pnobabitity
nathenatical
functions
Mathematics
of hypotheses,
and Statistics
and distribution
expectati.on,
of distributions.
variance,
prerequisite:
Mathenaticat
testing
to analysis
f _
function
of
and noment
cafculus
II
.
probability
and Statistics
of Mathematics 5S enphaEizing statistics.
estiEation,
intnoduction
for
Mathenatical
(nay be taken concurrently)
theory,
Statistics
of esti:ration
Concepts of probabitity,
Continuation
Conputer.
methods, negnession and correlation,
Mathenatics
generating
Laboratory
study of the binonial
appl-ications
non-pa!'ametric
place in society.
T$ro Hours,
to the area of statistics
departnents.
Conputers _ Capa_
programrning of a najon problen
of interest,
Mathenatics
tion
to Digital-
computers and their
conputer including
field
lntl.oduction
of hypothese,
of variance.
negression
prerequisite:
II
_
Sanpling
and correlation,
Mathenatics
SS.
APPENDTXB
,
PROGRAMS
RELATEDTO STATISTICSASSIGNED
I N M A T H2 7 , f 9 6 9 _ 7 0
1.
Write
a pr.ogran to process a deck of cards;
and standard deviation
and print
cofltpute the nean
the count, mean and standand
deviation.
2,
Write
a progr"aro that
reads N integer
80 to a card,
this
r.eads a value
values,
all
of N fr.on a card and then
between 0 and g inclusive,
The progran is to print
punched
the mode (or rnodes) of
6et of numbers and holr nany tirnes the rnode waa attained.
Wnite a proglarn that
a card followed
!'eads the number of observations
by N cards,
each containing
N from
a value of X and
the cornesponding value of y and cornputes the regnession
efficients,
the standard error
of correlation
for
of estimate
.,.,
and the coefficient
these data sets.
l + . Write a Subnoutine which accepts as inputs
values A(f),
an integer
subrqutine
N, N real
A(N), an integer M, and M boundary values
f o r a c o l " L e c t i o Do f f n e q u e n c y c l a s s e s , B ( 1 ) , . . . ,
i6 assuned that
co_
B(M).
the values of B are in ascending order,
is to leturn
to the calling
It
The
prognan the nean and
standard deviation of the values A, for each frequency class,
the number of data val-ues in that
data val-ues in that
class,
the percentage of
c1ass, and the cunul"ative per.centage of
data values up to and including
that class,
- 18 -
APPENDIX C
TIIE CENTRALLIMIT THEOREMAND UIXED DISTRTBUTIONS
:
iJeL ^f,^2,...,xn
dietribution
:
be a uandom sample
of
which has nean, U, and a finite
Let X = (1/n)
Xi.
-t
i=1
that
The Centr"at Linit
si?e
n from
variance,
a
o2.
Theoren etates
, \ - U
o / . tn
has a liniting
iance,
1.
nomal
distribution
(Let N(0r1)
denote this
!.rith rnean, O, and varEtandard nonnal distri-
bution. )
When n is
N(o,L)
is that
"suf,ficientl"y
larger'r
Wn has an approxlnate
A inuLe of thunb n that
dist!'ibution.
when n is larger
is ofte!
than about 25, Wn wi].l
used
appear to
have-a N(011) di6tribution.
Note that
say ver5f l-ittle
p1e is taken.
appLicable
of the Central
about the distribution
In particulan
to nixed
lle shall
clusion
the hypotheses
give
Lirnit
f)lon which
the CentraL Linit
Theor.en
the san_
Theoren is
dist!'ibutions.
an exanpLe which illustrates
of the Central
Limit
Theoren enpiricaLly
the con_
when the
- 1 9 -
sanpfe
for
is
this
taken
f,ron a nixed distribution.
exanple
was done
d- -h-
l. l.^- }n,a!
The sinulation
^^r
1 ^-^
vvrrsBr
5
_ LD | l
J-lJu
conPuter.
E)(AMPLE
Ro_1f a fain
l"et X equal this
spin a spinner
interval
value.
which selects
[0rl],
.If
If
the outcome is even,
the outcone is odd,
a nunben at randon fnon the
Let X equal the number selectld,
randqm vaniabLe,
tribution
olserved
die.
Xrdefined
The
by the 'rganerr has a nixed di6_
lrhich has a probability
of l/6
at each of the
lntegens 2r4, and 6, and has a unifonrn
density of l/2
the intervat
[0,].1.
The distribution
function of X i s d e f i n e d b y
x ( 0,
I (XJ
xl2,
0 3x
{ l r
rl 2,
! ! x
< 2 i
4t6,
2 a . x< \
5/6,
4 ix
1,
l
<6,
6 tx.
The tnean dnd vaniance of X ane defined by
s=/xdf(x)
1
I xl2 dx + 2 ( I / 6 ) + 4 ( 1 / 6 ) + 6 ( 1 / 6 )
v/+i
on
- 2 0 -
I
t
,
x - d F ( x ) - ( e / 4 )-
I
I0
x'/2
d x +. 4 ( 1 / 6 ) + 1 6 ( t / 6 ) + 3 6 ( 1 / 6 ) _ (
8 1 / 1 6)
7 r / 1 6.
. 6 !+ ^
v 1r^
w2,...,i{n
!1E
denote n plays of the
landon sarnpfe of size n from
the distribution
is-the
di.stribution
g a r n e r ! i, . e . ,
for
which F
fuirction.
shaLl use a chi-square
For sevenal va1les of n we
goodness of fit test to test
the
hypotheEis, H, that
l.In
= X- s/4
,rrfitrdttr
has a N(0,1) distribution.
Let the points -2.SS,_2,25,_1.95, ...r
2.25,2.5s
partiti.on the set of real nulbens into
]-9 intervals.
The
end intenvals are infinite
rays and the renaining L7 in_
tervalS a!'e of equal 1ength, .30. Let pi equal
the proba_
bllity
that Wn fal"Ls in the.irth
intenvaL lrhen H is true.
t ; . 9 , . , p 2 = P ( - 2 . 5 5 < W n s - 2 . 2 S ) , w h e nW n h a s a N ( 0 , 1 )
distribution.
We shal.L generate m = lO00 wn rs on the conputer
whele
'Let
each wn is based on n plays of the Igane.
Yg denote
"
the observed nuraben of wnrs in the i t t h i n t e r v a l .
Then
( Y r - 1 00 0 o : ) '
f000D.
has
approxinate chi-square distrj-buti.on with v = 1 8
-2t-
degrees of fneedom when H is
InEtead of setting
ror
a significance
each value of n betwe^-r , 4
three
independent
true.
chi_square
< u r ur c ,
levef
test,
J - n c . L u s f v e ,w e r a n
goodness of fit
based on a sampfe of size n = 1000
wnrs.
have necorded the calcufated
for this
tests,
edch
In tabfe 1we.
values of 12,
For this
chi_
square value we have also o e c o r d e d t h e ( l _ p ) , t h
quantite,
I.e., if U has a qhi-square distni.bution
Xt(p).
with v
degrees of freedom, then
p ( u 2 x 2 ( p ) )= p ,
l . r h e ne i s r e c o r d e d , 1 2 { p ) . . o o o s .
For this nrixed distnibution,
N(0r1.) distribution
when n is larger^ than about g or 9.
In order to show
graphically
lin to the N(0,1) distnibution,
we have graphed the priobability
N(0,1)
distribution
hiBtognan
chi-square
for
i{n appear"sto have a
the convqlgence of
in figunee L,2,3,
density
function
along with. the relative
each qet of data which yietded
values in table
t.
and 4
foti the
frequency
the star,tred
. 2 2 -
*'(n)
4
539.07
614.34
2rr7.60*
7 6 0. 2 2
189.49
7 6" 7 2
100.44
106.72
48.75
52.85
23 . 9 1 *
.158
48.17
.033
32,22
.021
t + 7. 7 6
.009
6
26.11
,097
29.66
.041
24.09
.152
9
11.?0
.862
2 7. 9 8
. 0 62
20.09{,
.328
15.48
.629
22.43
25"r+3
.11r+
? 9 .6 8
.041
.479
t3,23*
.778
.200
13,0r
11
1,)
2 2. ' 1 5
J.J
14
.449
r 8r+4
13.17
L9.88
'
*
48.61
TabLe
$ee frguneS Lr2,3, and 4.
1
25.53
.111
,063
1 3, 8 3
.7rt0
.r81
34,02
. 013
.340
24.38
.lrt3
-.?3-
N
ru
tl
lg
rr
5 t g
F d
'A
il
LJ
rfi
|l
2..
o
ri
ru
I
1 7 r u
3
',,
Ul
r*
A
H
o
6
tl
' z
- 25-
m
6
iri
tl
H
m
s
,,,
I
P
H f ,
u
o
tl
1..
- ?6 -
m
o
ll
i 9 O H H
i : 6
6
d
tl
2..
h
-2'l =
ORDERSTATISTICS
Let Yt, Y2, Y3, Yr be the order statistics
sar4ple of size 4 fron
val [0,1].
I.e.,
if
the uniform
xr,
on the inter-
x2, x3, xr are the observedsanple
v a - L u e s ,t h e n y 1 = m i n { x p
x3, x{}
distribution
of a randon
x2, x3, xr},
...,
y,, = nax {xl,
x2,
are the observed sarple values of the or.der statistics.
The probability
density functions
of the 4 order statis-
ti.cs are given by
gt (Yr)
4( 1-y, )r 1
g2 (y
!2y
2)
(y3 )
g!
gr (y4 )
0
1,
,)2 , 0
"(I-y
1 2 y ; ( l - y 3) ,
0
1,
4yl
1,
0 l Y q S ].
Each of these functions
is equal to zeno elsewher.e.
The probabifity
function
density
of the r.ange, R = Y{-Yl
is given by
h(n) = 121211-r),
03!St,
ze!'o elselrhere.
Eight
thousand sets of four
Eet repr"esenting
a nandom sample of size 4 fron
on the interval
tribution
oradet'ed from the snallest
of ordered numbers, five
run,
foun tests
range.
.05 for
priobabifities
tive
fo!
The interlval
of length
for
probabi.lity
numbers we]le generated,
[0,1].
the unifonm dis-
Each set of 4 nunbers was
to the fargest.
chi-square
Using the 8000 sets
goodness of fit
the order statistics
[0,1]
each
was par.titioned
tests
and one test
into
for
rnrere
the
subintervals
The theor.etical
each of the five
tests.
the subintervals
were found using the respec-
density
functions.
A good fit
was accepted
:r.
for
each test
at an q = .0S significance
rT sh rf ird6r nsa rc l r
clenst-tJr functt-ons
Y
rr'
v1 2 ' vr r ,
vr + ,
r
b
, 6^ r 7o , 8^,
level.
and g ane graphed the probability
and relative
frequency
and R, nespectively.
histograms
fou
ltt
u
. d
t
.
.
1
-32-
.
- 3 3-
- 3 +CONFIDENCEINTERVALS
.
L e L vx l , x 2 , . . . , x r D e t h e v a l u e s o f a random sample of
o
t a +
Size L0 fron a N(U,12.34) distnibution.
val
for
a particular
contain
it
sample thi6
i + 1 . 6 4 s 1 2 . 3 r + / 1 0. 1
interval
Hon'even, if
should be true
either
doe6, or does not,
rnany such intervaLs
that
about 908 of these intervals
two nandon Eanples of size 10 fr.on a N(40,12.34) diewere sirulated
on the conputer.
Fon each of these
52 randon sarnpLes, a got confidence
intetival
j.f the nean, l'l = 40, wene unknown.
In figune
52 intelvals
for
ltean.
were
the nean, U.
Fifty
tribution
1 . 6 4 s^ f ' 3 4 / n ,
the mean, u.
calcufated,
contain
inter-
the unknown mean, y, is
trfor
90ts confidence
is represented
the 52 calculated
by a horizontal
inter,vals,
was calculated
as
10 each of these
line.
r+6 ot' 88.5* contain
the
- 35-
iii
i l
]
.
5
)
Figure 10
APPENDIX D
Re'search and independent study projects
Hope Coll-ege
r
rao
yc4
v
Theoryrr:
in Statistical
The problern nay be stated:
nust decide which action
of actions
eituation
at
D.
Richard - "Critenia
L 9 5 5 - 1 " 9 6 6 : l^lepfer,
in Statiatics
Decision
A statistician
is to be selected
in order to do hinself
fron
a set
the most good in a
in which natu!'e may be in any one of sever-
al possibLe states.
The paper presents
and Bayesian decision
criteria
the nininax
and conpales their
use-
fulness,
1 9 6 7 - 1 9 6 8 : Gross, Deanna - "How Lange is Large Enough? A Study
of the Ramifications
Tlurough Sirulation
the validity
of the Central
Techniquesrr:
Linit
The paper" illustrates
and power of the Central
Linit
by neane of Monte Carlo techniques lrith
conputer".
shows that
for
diff,erent
Theoren
the IBM 1L30
distributions
sampLe sizes are necessary to justify
different
nornal
It
Theo!.en
(lhis
approximation.
the annual 1969 neeting
the Mathematical
paper was presented to
of the Michigan Chapter of
Association
of Ametica.
pa]]t of the resul-ts have been submitted
ican Statistician
a
In addition
to The Ane!'-
f or" publication.)
L968-1"969: Dj.ggelnann, Henry Wm. - "RandornNunber Generation
Chj.-square Testing'r:
The paper discussed pseudo-ran-
E=^.erators applicable
puter.
ip.r
(An articte
and
based on this
on the IBM tf30
con-
phase of the pro-
}lFs r'cen subrnitted to Corulunications of the
Association
for
of the project
Conputing Machinery.)
considered ,,amifications
Another phd.se
of the nule
- 3 1-
of thunb for
states
that
chi-square
the expected
ce11 should be at least
tang,
Patricia
goodness of fit
nunbeta of outcones
- !'Application
mean of a randon
distribution
trates
ioate
empirically
n fnorn a rnixed
distnibutions,
that
equal to 10,
acadernic cnedit
Mehnelt,
Elizabeth
Theorem to Discrete
t.I,, = Vn(X-u)/o
(Pal.t of the results
of
statistics
cLass.
of Central
Linit
was given,)
P. - r'Applications
and Existence
Distnibutions
of
to have an approximate no!.nal dis-
nean 0, vaniance 1, t{here X is the sanple
with rnean, u, and variance,
considered
1970(sunner);
when
to The American
me.rn of a randon sampLe fr:on a discrete
02,
distribution
The second topic
was an interpretation
means to
-tribution
I,
The paper conEiders the size of n necessary
tribution,
it
has an approx-
This wonk was conducted a6 a nesult
No extra
for
f9"
nean 0, and variance
of queGtions naised in a nathenatical
Meaaett:
o2.
paper iLlus-
this
Wrl = 'Ji(X--p ) /o
paper have been submitted
Stati6tician.
Linit
Let X be the sam-
sample of size
normal distribution,
n is at least
this
nixed
in each
of the Centraf
having nean, p, and var.iance,
tlro particulan
which
5.
Tlteorem to a Mixed Distribution'ri
ple
tests
say that. a nean and/or
enpirica]ly
of what
vaniance
of a dis-
does not exist.
Ne!rel1. Jovce - 'tEffects
In orlder to apply a t-test,
the sample is
of Round-off
on the t-test":
the population
flom which
taken is assurned to be nonnal.
In gen-
.
e!al,
live
_ 3q _
data has been rounded off
the sample has been taken fron
The effect
tion
of lound
variance
Monte Callo
off,
a discrete
as a function
and the sanple size,
techniques
so that
in effecr
population.
of the popula-
was studied
using
on the tBM 1130 conputer.
- 39 -
.
APPENDIXE
RESUMES
Dr. Elliot A. Tanis
Education:
B. A.
Centraf Colfege, Pe11a, Ioina, 1956.
University of Iowa, f960 (Mathenatics)
P h .D .
University of Iov/a, 1963 (Mathematics)
Thesis:
"Linear Forms in the Or.der Statistics
an Exponential Distribution'r
from
Teaching Experience:
Teaching Assistant, University of folra, 19S9-63.
Assistant Professor. of Mathenatics, University of
Nebraska, 1963-65.
Associate Professor of Mathenatics, Hope College,
1965 - Present.
other Experience:
U. S, Ar.ny, 1957 - 1959,
Associate Director,
NSf Sunneu lnstitute
for Advanced
Pl-acement Teachelts of Mathenatics, Hope College,
1967, 1968.
Dir"ector, NSf Suruner Institute
fo]] Advanced Placenent
Teachers of Mathematics, Hope College, 1969.
Lecturer, NSI Surnner Institute
for Advanced placenent
Teachens ^f
M.+}j6h:+i^c
rr^^6 .^rrege,
1968,
1970.
P n o fe s s i o n a f A f f i l i a t i o n s :
Menber of:
Mathematical Agsociation of America
Amenican MathematicaL Society
Institute
of MathenaticaL Statistics
American Statistical
As sociation
Society of Sigma Xi
lllD-L.LCataons:
rrAn Itex.ated Procedure for" Testing Equafity of SeveraExponential Distributionsrr,
Amer"ican -EoeE
Statistical
Journal,
volurne 58, 1963. (with Dr. EoEert-T.
rrlinear forras in the order Statistics
fron
Distribution,ii
The Annals
of
Mathenatical
Volurne35. 1964:-
ad Exponential
"A Randon Nuinber Generator hrhich Uses the Sun of Tr,ro
Congruential @nerators , rr subnitted to Conlunications of
the ACM,
"The Central Linit Theorem and Mixed Distributions
nitted to The A m e r i c a n S t a t i s t i c i a n .
.'r sub-
'rA Cand Matching Prob.lem,'r subnxitted
to the Mathematical
lec.
-l+0-
rrA Statistical
Hypothesis Test for the Classroomrrl
subrnitted to The
Mathenatics Teactrer,
Dr. Herbert
Education:
rfl.D.
L. Dershem
Univers-ity of Dayton, Dayton, Ohjo, 1965
ruroue Unaversaty, f967 (Computer Science)
Purdue Univeusity,
1969 (Cornputer Science)
Thesis:
"Approximation of Besselrs Differential
operator of fnactionaf
order by Finite
Difference Openators I
Teaching Experience:
Teaching Assistant, purdue University, 1968_69.
Assistant Professor of Mathenatics, h6pe Col1ege,
1969 - Present.
Other Experience:
Part time cornputer progranne!, University
of Dayton
Reaearch Institute,
1 9 6 1 - 1 " 9S
6.
Nunerical analyst, University
of Dayton Research Institute,
S u m h e r so f 1 9 6 5 - 6 2 .
Prof essional- Af f itiations
:
I,lenber of I
A,rerican Mathenaticaf Societv
Association for Computing Malhinery
Publications:
I'An Algonithrn for Approxinating the Solution
to a
Gene!.al fitist order System of Differential
Equations,'r
U D R I - T M - 6 7 - 1 3 7 ,U n i v e r s j . t y o f D a y t o n R e s e a r c h I n s t i t u t e ,
'lApproxination of the Bessel- Eigenval,ue
PLoblen by
F i n i t e - D i . f f e r e n c e s , ' l subnitted to SIAM J. Nuner.
1970.
" B e s s e 1 D i f f e r e n c e S ys t e m s o f f r a c t i o n a l
roitted to Math. Anaf. and A p p 1 ., 1 9 70 .
0rder ) " sub-
i
APPENDIX F
Hbpe Coltege Conputer, punch Card and Calculator
Equipnent
:
6
IBM 029 Card punches
I
IBM
59 Catid Vetrifie!
1
IBM
83 Card Sor:ter
1
IBM 519 Reproducing punch
I
IBM
L
Standard Register-Series
1
IBM 1131 CentraL priocessing Unit
I
IBM 1133 Muttiplex
1
IBI'{ 1442 Card Read punch
I
IBM L403 printen
I
IBM 2310 Disk Storage Unit
I
Calconp 565 Ptotter,
15
85 Collator
11,1E85 Electronic
1400 Burster
Contnol Enclosure
De6k CaLculatore
(prograromens)
6
IME 308 Digicorders
L
IBM Typewriter" printout
APPENDIX G
HOPECOLLEGE
Hope College is a four year,
-
stitution
nusic.
granting
undergr.aduate liberal
the degrees of bachefor
of arts
ants in_
and bachelor
of
Hope i6 fu11y acc!"edited by The North centrar- Association
of colleges
and seconda.r"yschoofs,
creditation
of Teachers Education.
and rhe National
councir
The cur,rent entoflment
for
Ac-
of Hope
is appr:oxinateLy 2r000 students.
The rnathematics depattnent
nembetrs, four
ing thein
of nine
of whon hold the ph.D. degree and two who ane cornpLet_
diesertation
for" the doctorate.
ated 9l+ najor'6 in the last
nathenatica
The depantnent has gradu_
S yeane - 28 of theee entered graduate
achool and 5 entered professional
junion-senion
of, Hope College consists
school.
najons enr"olled.
There ane currently
44
-ti3APPENDIXH
Xerox Copy of lndir.ect
and the Departrnent of
C o s t N e g o t i a t i o n A g r e e m e n r B e r w e e n H o p e C o J* c 6 e
Health ! Education and Welfane.
I|EGOTlATIOTI
J,CRE'}'ENT
-"
mSTtrTUIIoN: tlope College
nolland, l,Ilchigeo
49423
"-.AFdl.lB-_19L0_
Il,lI:C REF.: This retG;A
Negotla!ion Apreenent
da ted January-s, 19 70
SUR.'DCT: Indirect cost rate (s
) for use on gr€nts and contracts
wlth the
Departneor of Health, r . c u c aE
lon, and llelfare.
S[CTioll t:
Thf
and".S
contracts. rn"
rYPe
E q
Provlslonal
----=
::::,:,
";r;;.';;;:,"-*;.;;:";":;"":.r;:l;:::
*
-Bg!-9
9/L/69
U^tfL Anended45,37.
provtsronal elLl;e tJoErL
Anended
re.2t:
*8ase!
:;:i.,
Locarrons
On_Canpus
oii-dlilii!
All programs
iii il;il#;
Dlrect-aa1arle6 and rnagestncluallng vacatlon, holiday
and Elck pay, but
excludlng other frtnge beneflrs.
T)ceatnent of frlnge benefits:
Frlnge beneftts appltcable to alltect
- .na
lragea are tleated Es dlrect costs.
".t."fu"
l
I
I
Iull Il:
Thts Sectlon shat.i b c u s e d f o r processlng indirec t
cosc rafi!
publlc vouchers and re ports of e x p e n d i t u r e s .
Effcct lve Period
From
.Tvpe
Flnal
llnal
81na1.
llnal
Provislonal
*Base:
TrestIeot
9/L167
9/L/67
9lI/68
9/L/68
9/1/69 U^tfl
To
Rate*
Locatlon6
A p p lt c a b' e
1o
813r/68 44,Of/.
0n-Caooue
All Progra$s
8/3L/68 2r.7s/.
off-canius
All Prograer
8/3t/69 45.37.
On-carmus
A11 Prograr.s
Bnr/69 I9.ZZ
Orf-carpue
A11 Programs
Arreoded
Use retes, erc. ctteat ln Sectlon I above.
Sameas cl.ted ln Sectlon I above.
of frtnge beneflte:
SaEe as clted in Sectlon I.above.
For purFoses of deternining
indirect
costs to be applied to grani
I ft"egcittsu ir,el l se ,r n autti i. tviez i n s r a t e s c i t e d i n i i t s s e c t i i n ,
:t h: :e" :g: :r _
a n: ft e F" e
I
;;;;-r;';"";.::^;;;
DG\P SF I
5/29/69
lJhite
,:. S;Cttolt tII:
Sste AlternstlveE
onlyr and are Dot appll.cable to
the fotlolring rate altelnatlves are for use on 8g!g
The appllcation of th€ rates ln Sectlon lI to contracL6 will be governed by
contracts.
.the piovislonG of each contract.
The altehatl.ve ciled in Sectlon II together !'lth the
grantG.
lppllcable rate clted ln Sectlon Il shall be applled con6!etently to a1! DHEW
Alternatlve I
The rate established for the f,i6ca1 pellod to r{hLch the grant budget
yeat begins ntll be applled to the entlre grant budget year.
Alterngtlve 2. A 61n8le rste w111 be appl.ted to the enttre grant budget year and lhe
rate thaL rr111 be u6ed ls rhe one that tE effectlve for the longest pertod durlng Ehat
- bud8et year, If the budge.tyear fatl5 equally ln rno rate pertods, the rate of the
earller perlod vill be used.
Alternatlve 3. Ite rales e6tabllshed for the perlod6 to whtch direct expendttureo
are actually llade lri1t be applled to tho66 expendltures.
!p$!!!_!f1
A.
General
LIMITATIoNS! Use of the rate(6) contalned tn thla agreeDent ls subject to atly
appltcable
6tatutory o! admtnistratlve IlDltdt{ons,
Acceptance of the rate(s)
..
atreed to herein 1s prediiated upon the condl.tlons:(t) that no costs other than
' tho6e lncutred by the grantee/conbractor r€re tncluded tn
tt6 lndirect co6t raie
proposal and lhat such cost6 sre legal. obllgatton8 of the grantee /contractor r
(2) that the same cost6 that have been tleated a6 tndl.lect cogt8 have not been
claloed a8 dlrect co6t6, and (3) that sloila! types of co6t6 have b€en accorded
. conslstent trealEent.
ACCOIJNTINC
CEANGES:If a predeterElned rafe(a) te contatned tn tht6 agleenent lt
lr based on the accountlng systern lh effect 6t the ttEe the proposal rlas 6ubDttted,
ChanSe6to the method of sccountlng, lncludlng but not ltotted to,
' chanSes 1n chdrglng
a pattlculat type of cost f,ro!| lndlrect to dlrect, lequlre
. the prlor approval of, the D1lectot of cranrs Adrolnlstratl.on policyr IttEH. Falture
to obtaln 6uch approval $ay result ln 6ubsequentaudl.t dlSallowance6.
c.
NOTIFIO\TIONTO FEDEML ACENCIES
I Copte8 of thls docuDent D6y be plovlded to
other Federal offlces 66 a Dean6o! notlfytng theo of the sgreeDent contalned
her€1n.
D.
SIECIAL RENARKS:
}:one
Grantee '
8y
,4lfe r! G. SlrscheD&aoo, Chlef
Cost Pollcy & Rate Negotlatloa
Date
4 1 : . . 2 .t"t , n . . .
lfegotlated by
q. leldmar
Telephone 2o2 962'8334
Eraacb
- 4 6 i
nETERENCES
Appefbaum, Mar'k I.
.,
an.t cuthrie,
i,Use of Computer.s
in Undergrad_
uate Statistics
Instructionrr
proceedings of
a Confenence on CoroDuters
in the Undergraduate Curnicula,
?he University of loi/a, fS70: pp.
2.1_
2.3.
Cooley, Willian
W,
Donald.
" C o n p u t e r - A ss i s t e d I n s t r u c t i o n
in Statistics,,,
Stat_
Coxnputation, Acadenic press, New york,
1969.
'TSAMDS,A program
Gan!'ett, Henry c.
to Generate Empirical Sampling Dis_
tributions
of the Meanr" proceedings of a Confenence
on Conputels in
the ltndergraduate Curricula, The University
of jolia, Ig70, pp. 2.32_
2.38.
istical
Gilgen,
Albe!.t
R, and Hall,
Expenirnental Design,"
Michael A.
proceedings
the Undergraduate Curricula,
', Conputer_As
sisted
Teaching of
of a conference on gonD'teis
The University
in
of lowa, 1970, pp. 2.39-
2.46.
'rThe Computer as
an Instnuctional
Koh, Young 0.
Courser'
Proceedings
Toot for
the Statistics
of a Confenence on Conputens in the Undergnadu_
ate Curri.cuta, The Univer"sity of Iowa, 1970, pp. 2.4_2.I7.
Lohnes, Paul R. and Cooley, Willian
W.
Introduction
to Statistical
Procedures: qrith CornputerExercises, John Wiley t Sons, fnc.,
New
York, 1968.
Sterling,
Theodor D. and pollack,
Teach Introductory
Statistics,r'
Seynour V,
'ruse of the Conrputer
to
Comrnunication of tne A ss o c i a t i o n
for. Conputing Machine:ry, g, 4 (1966), pp. 21+_279.
ster"ling,
Theodor. D. and pol1ack,
Data Processing.
seymour v.
rntroduction
to statistical
P r e n t i c e - H a 1 1 , E n g l e w o o d - C l i f f s , N e r ^.,r e r s e v . 1 9 6 8 .
. wallace,
David L.
rcompr.rtens
Are the Main Effects?"
New york,
Wikoff,
in the Teaching of Statistics:
Statistical
Richard i.
icula,
CorAputation, Acadeni.c pness,
L969.
',Using the
Computer in Basic Statj.stics
Pnoceedi.ngs of a Conference
Cu
!,lhetre
The Unive?sity
on Conputers
Courses,,,
in the Undergnaduate
of lowa, lg70, pp, 2.!a_2,2U.
I
Techtieal
Na.ne of Institution:
Addreas:
Principal
Gratt
Period
fnvestigatora:
Nunber:
eoveled
Suenar5f Report
Hope ColleEe
Holtand, Michigan
49423
EUiot A. Tanis
He!'be!,t L. Derahem
c,J.- 28786
by grant:
esrg,
rrrr
Eo August,
Intrioduction
the Statistics
of
1973
the Computer Ln
CunnicuLurn
SUM}IARY
The purpose of this
being deveoLped for
a way that
grant
an intnoduql6ry
the student
so that
illustrated
(ii)
the Lateot
Materials
_(i)
statistics
are
course in such
always has lear.'ned enough progranming
pnogran the next statistics
tics
is tlrofold:
technique
and knows enough stati.s_
programning pninciples
by examples involving
to
previously
lea!,ned car be
fearned statistics.
Materials
ar.e being developed for a Laboratory
for a
two semester junior:-senior, leve1 mathenatical
probability
and
6tati€tic6
counae in whlch students have the opportunity
of in_
crea6ing thein understanding and appreciation
of the theorv bv
perfonning simulations on the conputen.
,
During the suruner of lgli
along with
four
supporting
software
pnofessor"s Dershen a n d
Tanis,
capable students
for
wnote exercises
and devefoped
our IBM t13O computer:
During the 1971-72 acadenic yean the course changes wer"e
intnoduced
into
our" curniculum.
The reaction
of the students
to
both courses was favorable.
l,latetrials
rnen of 1972.
for
linited
for
By the end of this
use in other
l-ar these natelial"s
tors
fron
both courses are being nevised duning the sum_
other
supported by this
wil1
colleges
be available
and universities.
be shaled with
institutions
grant.
suruner they will
appr.oximately
In particu_
S0 educa_
at a Confer"ence in August which is
Peraonlrel
The follo!,ring
by this
professors
are associated
with
and suppo!,ted
grant I
.
Dr, Hetrbert
of Matheaatics,
L. Oersfreur, Assistant
profeasor
Hope ColLege.
Dr, Elliot
pnofesaot
A. Tanis,
of Mathenatics,
Hope Co1]ege.
The following
atudenta neceived Bupport ;uring
the sunmer
of 1971 and the 19?1-72 acadenic yean:
tynn Klaasen Hil-legonds
Timothy
Hiltegonds
Richard
pohl
:
-
Glenn weener
The following
.!
student8 ane receiving
support during the
surnmerof I972 !
Roger Crj.srnan
Richard Meyens
GaiI Ringsnith
Paper6
The following
paper.s were plesented
on. Conputers in Undergraduate Curricufa
1!gg
of that
Confe!,ence.
at the L9?2 Conferenee
and appear in the praceed_
rrA Course on
Conputing and Statistics for
Social Science Students", by Herbert
L. Dershen
rrTheory of probability
and Statistic8
lLlustra_
ted by the Computerr', by Euiot A. Tanis
Confe:rence
A Sunnen cgnf,erence for
callege
teacherE of mathenatics
on
the use of the eonputer in the undetrgnaduate stati8tics
cunricu_
Iun wilL be heLd August 1 4 - L 8 , 1 9 ? 2 . T h i s c o n f e r e n c e
is being
Bupported by thie gnant. Dutring thie conference
we wiLl
Bhare
ou:r expeniences.
fZ?,,t a, f;.--v
A/,.-- 2V, tf fl
_--==i:-
- <qi1
ANNUAI.,PROGRESSREPORT
. ,-rul, I, 1972_June3 0 , 1 9 7 3
Nane of Institution:
Aqclre a s :
Principal
Investigatora
Gr.ant Nunber,:
Period
Iltle
\
,
\
\
Covered by 6rant:
I
Hope College
Bor-land, Michigan 19423
:
.E]l-iot A. Tanis
EerDert L. Derrahem
G,I - 28?86
.tune, I97l
to AuguEt, 197A
lntroduction
of, the Conputer
rlr lne statiatics
Cu:rniculum
1) HIGHLIGHTSOF PROJTCT
ACTIVITY
A conference held or
college canpus on
"nt ""nt
August 14-18, 1972 was
-at:tended by 52 college
teachers of
statistics
fron throughout the
Midr./est, . At this
conference
the philosophy and
the materials
of the two cour.ses
devefop_
ed under this grant
were presented to the
panticipants
in
f,orma1 sessions.
During nore infornal_
seesions, the parti_
cipants wene invited
to neact to the naterial
ard nake suggestions for inpnovenent.
Copies of aL1 natenial
devetoped,
ancLuding exencises, prograrn
descniptions and program
print_
outa, wene given to
afl participants.
In addition,
materials
r"ere sent to over" ZO
othef educators thnoughout
the country
by speciaL request.
Duning the 1972_73 acadenic year,
counses for
gt'art
rlrh.ich naterial
we)ie taught
is being developed under thi6
fon the second time by professons
and Dersherr using the nodifications
ing sururen'
rn addition'
raany of the panticipants
A repolit
of this
the annual neeting
ticaL
Association
A report
part
Tanis
made dur.ing the precea_
of the nater.iar.s wer.e used bv
in the Sunner Conference.
ploject
iras made by Dn. Dershen at
of the Michigan Section of the
Matherna_
of Aner.ica on May 4, 1923.
of this
Four:th Conference
the two etatistics
project
on Conputers
was nade by Dr. Tanis at the
in the Undengraduate
at the Claremont Colfeges on
rlune 20, 1973,
A Senior Honons projectr
which nade extensive
Curricula
use of the
cornputer software
deveioped in this
ploject,
was compLeted
by Roger Cnisman, one
of oun nathenatics iajors.
A final revision of naterials
and pteparation
for
dissemination is being carliied
out during the sun[ner of
]-973.
In addition,
reactions are being coflected
from those edu_
cators !.tho used the naterial
this past year.
2) PUBLIC INFORMATION
RELEASE
In order
ucation'
it
to effectively
use a computer as an aid in ed_
is necessany to devel.p
and pnograns fon the conputer.
material"s,
fron
they need tine
the National
futut?e students
ceive a berter
in addition
at Hope and other
the tine
institutions
a couLse was deveLoped for
dents in the soci.al sciences.
is now an integral
j.ll-ustrate
This grant
fox"
at Hope College to wonk together
progranming and statistics
statistics
to ability,
so
wj.ll
re_
educarion.
In particular
puter
For educatons to deveLop these
Science Foundation provided
Pt"ofessons and students
that
both course rnatenials
part
teaching
in an integrated
In addition
com_
way to stu_
a laboratory,
of a rnathematical pnobability
whlch
and
course,
rrras deveLoped which uses the conputer to
empirically
many theoletical
resul-ts.
3) PERSONNEL
The folLowing
ed by this
grant:
pnofessors
a:re associated with and supponr-
.
Dr. Herbei.t L., Delshen,
Aseociate
pr.ofessor"
of Mathernatics, Hope
CoLlege.
Dr. El1iot A. Tanis, profeseor
of
Mathenatics, Hope
Co1lege.
The following
Etuden
xneror rezl a,'atne rszr_l;
duninsthe eum":"."J:;":::-
Lynn Klaasen HiUdgonds
Tinothy
Hillegonds
Richard pohl
Glen Weener
The follor{ing
studentg
received
eupport during
nen of L972 and the 19?2_73
acadenic year:
the €uln_
Rogen Crisnan
The following
Richard
Meyere
student
!,eceived support
during
the eun_
netr of L972:
cait
The following
pnofessor
Ringsnith
Buis
is neceiving
suppolit during
the sunmer
of L9?3:
profeasor
Mathenatics,
John T. Whittle,
Assistant
priofessolr of
Hope Col"lege.
4) PUBLICATIONS
Tanis,
Elliot
Iflustrated
A,,
rrTheory of probability
and Statistics
by tlle Conputer,,, proceedings
Confele;nce on ComDuters
in
Under,graduate
of The 19?2
Cu:,:ricula,
' l
At1anta, Georgia, 1972, pp.
S13_S20,
Dershen, Herbelt L., rrA
Course on Computing and
Statlstics
for Sociat Science Studentsr,r proceedings
of The t9Z2
Conference on ConDuters
in Undengnaduate Curricula,
Atlanta, Georgia, 19?2, pp.
52S_S2g.
T.'ri6'
Elriot
A.r
Pnobability
"A Conputer Labonatory for
and Statietics,r,
proee;dj4gB
Mathenaticar
of a Fourth
Confenence on Conputer s in the
Undergnaduate Cur,t?icul a,
Clarenont, California, l9?3, pp. q16_426.
r##t(;k!*
Course on Computing and Statistics
for Social Science Students
Herbert !. Dersh€in
Department of lvtather,latic6
flope College
Holland, I{ichigan
616 392_5717
origin
of the course.
4p42J
Bef,ore the lntroductlon
of
the course to be descrj,bed in this paper,
rnost economics
and social science students at Hope
College enrolled
ln two nathematics courses. These ,,rere
introductory
statistics
and conputer programming. In the
acadenic
year 7969-70 two developnents
occurred which pointed
to the advisabil,lty of conbining these
courses.
First,
Dr. Jay lolkert
conducted experimentaL
sectlo$s of the lntroductory itatistics
course at Hope
CoLlege in which he used the computer
as a tool to
obtain illustrative
information.
He did this by
aUowing stridents to use previously written
prograns
prepared data decks.
fhis
on
was done in conjuction with
the project
to study the use of the computer in
E t a t i s t i c a l i n s t r u c t i o n s p o n s o r e db y
the National Science
Foundation and the University of North Carofina,
iri
which Dr. Folkert was a participant.
At the cl-ose of
the experirnentit was Dr. Folkertrs feelins
that the
conputer was an asset in such a course
but that somethlng
was fost because the students were not
able to participate
in the preparation of the
lrograms.
Herbert L. Dershen
At the sane tlne,
a course on conputing f,or social
science students was i.ntrqduced into
the Hope curricuLum.
This course j.s basicaUy a FORfRANprogranning
course.
Those who were inyolved with teaching
this course .found
that 6one knowl,edgeof statistics
would be valuable to
those students enrolled.
With sone statis.tics background,
the students coutd be assign€d projects
their fields
pertinent
to
of interest.
It was therefore the consensus of the Hope
College
mathematics departnent that it would be nore
valuable
to combine statistics
and coroputer programning into
one course for social science students rather
than to
continue with two separate coursea. A proposal was
nade in the Faf1 of 19ZO to the National Sclence
Foundation
f,or the development of such a course, in conjunction l{ith
the development of a ]aboratory for the nathexnaticaL
probability and statistics
course, and this project
was fun ded".
Value of the cornputer. There are three najor
reasons that the conputer is an asset to the introducrory
statistics
courge. First, exposure to the computer and
conputing is a necessary experience for any social scrence
studento He should be aware of the economic,socioloeical
and pEychologicaf impacts of the computer as weLl- as
the applieatlon of the cor0puter to the soLution of
problens in his disc ipLine.
Herbert l.
Dershen
Seconalr the conputer can serve as
an ald in
teachlng statistics
theory.
0he student has a nuch
g?€ater nastery of a concept
after he has explained it
to sorneone e1ae. when a student
wrl-tes a progran he is
doing just this, explaining to
the computer how to
€olve the problen.
For exanple, in the assignment shbwn
in Figure 3, the student is
asked to explain to the
conputer how to test hypotheses.
Also the eomputer can
be used to provide the student
with illustrations
whlch further €nhance his understandLng.
An exanple
of this ls found in the assignrnent
given in Figule Z in
which the student ls a6ked to
tllustrate
the normal
approxlmatlon to the binonial.
Thlrd,
th€ conputer allows the student
to app]y the
statistical
plocedures he is 1earnlng
to useful aets
of datar thus giving hlrn valuable
experience in
lnterpretin€i results and an interesting
incentive for
learnlng the statistics.
Description
is entitled
of the course.
,'Applied Statistics
The only prerequisite
The course being devetoped
and Computer prograrnming.,,
is high school algebra.
It
is
a two senster course for three hours credit
each
senester. An outline of the topics presented
in the
course is found in Figure 1.
The students are i.ntroduced to a sinplified
forn
of input and output so that they can
begin progranrains
wlthout being exposed to FORIIIAT
stalenents. . fhis is
done by subroutines written
for this course because
Hope CoJlege has an fBM
1130 which has no simptified
Herbert I,. Dershen
lnput/output
i.ncluded ln the systen.
The author has
notes to serve as a text for
the class for the
FoRTRAN
portion of the course
because existing texts
present the language in
a sequence dif,f,erent llon
that
deternined to be optirial
for this course. For exampte,
we present subEcripted variableg
very early ln the
course because thay are ne€ded
to program examples and
procedures in descrlptlve
I tatlstics.
The statistlce
text chosen i6 Elementarv Statistics
by Paul c. Hoel, and the topics
covered fol.lov, the
presentation of the tExt
wlth exc€ptlons noted be1ow.
Descriptive Etatietlcs and probablllty
are reversed in
order that the students nay gain
Bore famlllarity
with
IoRTRANand subscrlpted variables
before they are
Irepared
needed for descriptlve
statistics.
Sone discusslon ts
added conc€r.ning random number generators
al"ong wlth
'
experlence ln theLr uae when randon sampling
is treated.
Also, the students are glven practlce
in using carmed
subroutines ahd lnterpreting
and analysis
llve
their
results
for regression
of variance.
data set6, each consisting
of, several variables,
are stored on a disk.
The students learn early in the
course how to access this data. These
sets are data
actually
used for research purposes in the areas
of
sociolory' psychology, education
and economlcs, and have
been contributed by facuLty on the
Hope canpus f,ron their
research and fron other books
and articles.
Already
three additional
sets have been contributed
for next year.
Helbert
L. Dershen
Each stud.ent is assigned one
data set and one variable
fron that set which he usels
throughout the year.
This
us€ ranges fron findina
the nean and standard deviation
t o taking randon samples
to obtain confidence
t o coEeLation
intervals
and regression with other
variables
the sarnedata set.
in
The students work fewer
textbook problens than
in
the standard statistics
course. Instead, they write.
computer progratns for soLving
these problerns and then
apply these prograns to their
data sets.
The Etudenrs
are given a total of 25
assigrunents involving the
computer
throughout the year. ?hi
thanoneassienment
r", """;:"T;:""::IJ":::-:J:1"1::;
involve the writing
of a progam, the application
of that
prog"anr ?nd the sngrreling
of some questions intended
to
bring out the important points.
In nany cases students
are asked to punch.cards sumnarizing
their
results so
that a nean re6u1t may be obtained
for the entire class.
Extra credit problems are given
atong with each assignnent
to challenge the better students.
Two sanple assigrunents
are found in Figures 2 and
3.
DescriDtion of the projecl.
The project for
developing this course is of tv/o years
duration. In
the sumner of 19?1 this course was
organized with the
assi.stance of four senior r0athenatics
najors who
wlote the necessary subroutines
and progranming
exanpLes as well as testing
the corlputer assigmnents.
Herbelt
L. Dershen
fhe course is being taught for
. acadernic yea]. l9?l-ZZ,r{ith
26 students.
the first
a starting
fhe sunner of 1922 wiU
tine
in the
enrollnent
of
be devoted to
revising
the course according to the
experience gained
during the preceding acadenic year.
fhe course will
then be taught in revised forn
during the academic
yeat 7972-Zj and the following
sunner a f,j-nal report
wir'r be nade atong with the final preparation
of nateriars
such as course outline, Lecture
notes and aa6ignments.
These nateriaLs will be distributed
to allow other
staff nenbers to teach the course.
ResuLts,
f,lrst
At this v/ritlng
it
is the niddle of the
year of the project
and hence too early for any
flrn dlscussion of resuLts.
Thus f€r the reaction of the
students has been most f,avorable. Some
have indicated
that they feel the statistics
is nade easier to
understand by the use of the computer.
I suspect,
however, that there are others for whom
the computer
sinply cl.ouds the issue. Xlore students
have been
conpleting the extra credit portion of the
assiglments
than was expected.
The author feels that the morafe and interest
of the
students is !.'ruc
h greater in this course than in eithex
of
the two parent courses, and for this reason,
the course
is a pleasure to teach. There has al.so
been a favorable
response to this
who fee], it
course from our social. science faculty
is a nost va.luable course and
are encouraging
their students to take it
as well as assisting
developnent.
us in its
I'
He"bert !.
First
fntroduction
2.
Dershen
7
Senesrer
to conputers _ Conluters,
algorithns, languages.
roRrRAN
_ .o":l1ll:,
31:l::l:_:t
srarements, transfer
variables,
statemenrs, s j.mpLified assisnnen.r
inpui/ou.cput.
Probability - Rutes of probability,
)t
counti.ng techniquues
4 . Subscripted variables
Descriptive statlstics
- F
standaida""ijii"^",.iirJ".;:lffffg..rstributions,
nean,
IuneDyshevrs
I:P:!,111lv distributions - Discrete, continuous.
inequality,
BinonLaJ-, Normaf.
7 . Randomsanpling - Randomnumber generators,
sampfe neans.
Subprograns - Ilnctions,
subroutines.
9 . 9ll':l_ cgmpuler languages and.systems _
COBOr,,tist
p"ocessing lanquaees ind tl
timesnarrng, man-machine
int"";:+I"ilplications'
Second Semester
1. Input/Output - FORMAT
srarenents.
2. Estination
- Conf,idence intervals,
3" lesting. Hypotheses - Type I and II
neans, testing proportions.
t-distribution.
errors,
4. Correlation and regression _ tllultiple
non-linear regression, interpretation
testins
linear
- ; ; ; u iregression,
;;:.
of
5. Multiple subscripts
6. Chi-square - Cbntingency tables,
goodness of fit.
7. Analysis of variance - use of library prograrns.
B. Nonparametric tests - Sign test, rank_sun
test.
9. lliscellaneous -.Implications
of cor0puters, experinnental
qesrgn, srmulati on.
Iigure
1.
OutLine of the course.
l{erbert
L. Dershem
Purposer The purpose of, this
assigrunent is to illustrate
how the norrnal distri.butic
In can be used as an
approxination
to the binonial, when the
approxination is good,
and how
to use the nornal table progran
XNORM.
lescriptiont
Write a prog"am which
reads n and p and
using subprog"an BINOM
computes the binomial probability
that x = k for k = 0,1,...,n,
and the nornal probability
that k - * S *
S k + * f,or the nornal distribution
*ith
mean np and variance np(f-p),
and the sane values of k.
Use XNoRI!,I
described in Appendix E to
f,ind the nornal probabiLity.
lutput r The output is to consist
of one line containing n,
one containing p, folLowed by
n+1 lines each containing
a value of k, the corresponding
binorniat probability
and
the nornal probabil.ity.
Questionst 1. try out your proglam
for a variety of,
values of n and p. Do the cases
where np and n(1_p)
are both greater than
5 show good accuracy? How is the
accuracy when the above m1e is viofated?
2. Does the accuracy of the approximation
tend to varv
with k for fixed n and p? If so,
how?
3. Do you notice that one probability
Tnan the other?
is always larEer
Can you explain this?
Exlra thinEs to IIX| ifrite a program
which is the sane as
the one descrj.bed above but which conputes
the probability
that x < k instead of x = k. Ans
er questions 1_3 for this
program.
Iigure 2.
sanple Assigrunent
Normal Approximation to the
Binornial
Herbert L. Dershexn
9
Purlose r The purpose of this assignnent
is to j.ntroduce
the student to testing a hypoth€sis
about a sample nean
and illustrate
type I and type II er"ors.
Descriptiont
write a functi.on subprogram
which has the
folloning argumentsr XMUO,ths
hypothesized mean, XUU,
the actual nean, SIC the actual. standard
deviation, and
Nr the sample size.
The subprogran is to generate
1oo
samples of size N fron a norrnaL
distri.bution with nean
XMUand standard deviation SfG.
t'or each sartp::e, a 95%
confidence j.nterval is constructed assuning
sigma knov.n,
and a test is nade as to whethe! XI1UO
is in the confldence
l n t e r v a l - ' i . e . ' w h e t h e r / A = X I W Oi s
accepted. A counr
i s m a d eo f t h e n u n b e r o f t i n e s t h e h y p o t h e s i s
is accepted
fhls ls the value to be returned for the function.
write a ca]ling
progran which calls
thls
function
four
tirnes, each ,tine with XMUO=ZO
S,I G = 5 , N = 1 0 , a n d f o r
xl/].n=20
,22 ,25 t3A ,
qhg!
r Your output should consist of XMUo,xlv:UrsIC,
N and the value of the function for each call
of the function.
Questionst 1. Relate the results of each caLl to function
to either type I or type II errors.
Specify which.
2 . P u n c h a c a r d s u r n r a a r i z i n gy o u r r e s u l t s .
3, Ithat woutd be the effect on your answers if SIc were
10 instead of 5? What if N were 20 instead of 10?
What if
we used a 99% lnsi.eaa o! 95% confidence intervat?
Fieure ,.,
SampleAssignnent
Testing of J{ypotheses
llerbert
o. Conpute the theoreticalerror
I,. Dershen
probabillty
10
of making an
ln each of the f,our perforned
tesr6 of hJDotheses.
Indri.iat€ f,or each, whgther.
it ts a type I o, a typ€
II
error.
Compare these rvith your rtisults.
5. the above prog?an t€ste the hypotheels^
= ZO
against the two_sided alternatlve
/l. / 20. Fow woul.d
your anawors b€ chang€d
if a on€_sld.eal alternatlve
.
> 20 were uged? What It
/t
/L< ZO were the alternativ€?
Extra thlnas .E trvt Add enough
genelality to your
p"ogran that you can try aone
of the thlngs suggested
ln questlons 3 and 5 above.
Flgure 3 (cont.)
sanple Assignnent
r
!
FINAL TECHN]CAI REPORT
Name of Institution:
Address I
Prinqipaf
grant
Feriod
r r.IJ.e :
Inve€tigators
Hope Collese
Holland, Michigan
:
Number:
Covered by G?ant r
49423
Elliot
A. Taais
Herbert L. Den6hero
G , J- 2 8 ? 8 6
JWle, 197L to Augu6t, 1973
fnttroduction of the ConDuter
r-n the Statisties
Cunrilulurn
1)
BRIEF DESCRIPTTON
OF PROJECT
The purpose of this
developed for
gr,ant $ras twofold:
an integrated
prograruning fon social
(i)
course in stat_istics
science
students.
is
MarerraLs.wene
ancl cornputer
The goal of the counse
to use each of these two subjects
as an aid in teaching
other.
(ii)
Materiaj-s were developed
for a fabotiatory for
two senester junior,_senior
l"evel nathematical probabtfity
statistics
course.
In this
opportunity
to increase
the theory
by perforning
their
laboratory
the students
four
supporting
software
Duling
a
and
have the
under"standing and apptleciation
simulations
capable students,
of
on the conpute!..
Duning the sullunenof L97l professors
afong with
the
Dershen and Tanis,
wl.ote exercises
and developed
for" our" IBM 1130 conputer.
the igTl-22
i.ntroduced into
acadeni.c yea! the course changes
were
outr curriculurn.
The foun students continued
to help us inplernent the changes,
Materials
for
both courses were r^evised duning the suruner
of )"972, Three Etudents assisted duning
this
sunner-
A conference lias held on the Hope College campus
August
14-18, 1972, which was attended by 52 college
teachers of
statistics
fron throughout the Midwest.
At this conference
the philosophy and the materiafs of the two
courses developed
under this grant r,rere presented to the participants
in formaf
sessions.
D u r i n g m o r . ei n f o r m a l s e s s i o n s , t h e p a r t i c i p a n t s
were invited
for
to react
improvement.
exercases,
to the nateriaLs
and nake suggestions
Copies of al1 materials
developed,
program descta,iptiolls and program pt"intouts,
given to al_l participants.
including
were
, u r 1 n g l n e _ 1 9 / z _ 7 3a c a d e n i c y e a r , , t h e t w o
statistics
colrrses were taught for the second time
by professot,s Dershern
and Tanis using the rnodifications
made during the preceding
6U4mer.
A final
revision
made during
assisted
the sunmer of 1973.
Plofessors
materials
statistics
into
the computer assignnents
the exer.cises for
was
John Whitt]"e
this
revision,
two separate rnanuals.
The
One
fon the applied
and computer prograruning course.
statistics
2)
professor
Dershern and Tanis with
wer"e collected
hanual contains
contains
of the newfy developed materials
the mathemati6al
The other nanuaL
probability
ard
labonatory.
PUBLICATIONS
Tanis,
ELliot
A.,
"Theot'y of pnobabifity
and Statistics
Conference on Conputers in Undergraduate
Cunricula,
Atlanta, Georgia, L972, pp. .S1g_S20.
Dershem, He!"bert L. , A Course on Conputing
and S t a t i s t i c s
for
Social Science Students,!' proceedines of
The 1972
Confer.ence on Conputers in Undergraduate C u r n i c u l a ,
Atlanta,
Tanis,
El-l,iot
Georgia, l-972, pp. S25_528.
A.,
Probabi-lity
ltA Coroputer Laboratory
and Statistics,r'
Clar.emont, Califonnia,
Tanis,
E1liot
tribution
for
MathematLcal
proceedings of a Fourth
1973, pp. 416_426.
A, and Crisman, Roger, rTwo Nor]lal Dis_
Problems with
the Sa.ne Solutionr!'
to The American Star is ti cian.
subnitted
Tanis , Elliot
A.,
r'Mathematical
bability
Computer Laboratory, r' subnitt
Confelence On Computers in
Hi
REPORT
S
.
and Stati6tics
d to the First
British
r" Education.
Both Dr.. Delshen and D!,.
Tani6 gave a report of thj.s
Proj ect
at a Gr"eat Lakes Colleges Association
C
uting Symposium
I'hich
was hel-d Malch
Thnee of
the
7_g,
papers
:-g72, at Wabas
listed
Col1ege.
above ere e presented
at the
Conference€ on Conputers in Undergraduat
Curr"icula held in
AtLanta in 1972 and in Clarenont
in 1973
Dr. Derishen rlade a repolt
neeting
of
the Michj"gan Section
of A&erica in May, 1973.
one of our €tudents,
nade extensive
4)
of this
of, the
At this
de8cribed
sane
his
at the annual
thenatical
Association
eting Rogen Cr.isnan,
Senio
use of the conputeta softw
Honors Pr.oject vrhich
e developed
in
thig
PERSONNEL
The following
this
professore
were
ted with
and suppo!,ted by
grant I
tler.be:rt L. Dershern,
Dr.
Professon of Mathenatics,
Dr3, Elliot
of
The folloqring
of
oject
f971 and the
A. tanis,
I'Iathe&atics,
students
Ho e C o l l e g e .
pro e a s o r
Hope C
neceived
Lynn Klaasen Hillegonds
Richard Pohl
Glen Weener..
1ege.
supp r't
19?l--?2 academic year:
Tirnothy Hillegonds
sociate
during
the summer
The folfowing
students
received
support
during
the sunLter
o f 1 9 7 2 and the 1922-73 academic
yea!:
Roger Crismai
Richard Meyers
The fol-lorning student
received
suppol.t during
the summen
of 19?2:
Gail
The fol_fowing
Ringsmith
Buis
Professor
received
profeesor
John T. t\rhittfe,
suppont duriing the su[[ner.
of
Assistant
pnofessor
of Mathenatics,
Hope College.
5)
uult computen center
this
staff
wa6 very coopenative
th!,oughout
project.
Dur.ing the development of the conputer
soft\rarie,
the conputer center contr.ibuted 190,471
hours of tine at $30
pe! hour,. This anounta to a contibution
of gS,7L4.13.
.qs stated
earlier,
the
S2 conference participants
a complete set of outi rnateriafs.
natelia1s
two foreign
to ove! 25 educators
In addition
thnoughout this
!eceived
we have sent
country
and i.n
countriea.
During the cuxlnent acadenic year two of ou!,
colledgues,
Professors John hthittle and Jay Fotkent,
ane using ou! naterial_s.
Their experiences will be helpful in future
revision€_.
Both Dr. De:.shen and Dr. Tanis plan to
subni.t repotits to
the NationaL Technical Information
Service of the Depdrrnent
of Coinmerceto facilitate
wide:r dissemination of our resu-Lts.
Hope Coflege is cu!,rently
which has time sharing
of our. nateniaLs
installing
capabilities.
alle applropt iate
for
a Xerox Signa 6 conputer"
We plan to determine
whi.ch
use with
terninal-s
then nake the neqgss4r,y adaptatlons.
We believe
successful.
that
both parts
of
of his
up his
l"abonatory naterials
a conpanian textbook
Hogg fron
have been
to COUPUTeat Dartmouth
fon
faborato!5/ naterials
for publica_
and hence i,rider dissenination.
a revision
projeet
Dr. Dershem has applied
the puppose of h,riting
tion
of this
and
the University
Dr. Tanie pLans to publish
after
lrhich he is wniting
the conpletion
with
D!,. Robert V.
of, lowa.
{lt*tafu
ElLiot
A. Tanis
Herbent L , D e r s h e n
Novenber 16, 19?3
Date
FINAL BUDGETREPORT
Nane of fnstitution:
Principal
Investigatons
Hope Collese
Holland, Michigan
:
Elliot
A. Tanis
Herbent L. Delshexl
Gratt
Nunber I
Peniod covered by grant I
A.
r.lg423
G J -2 8 7 8 6
,iune 1971 to August 1973
,LnEroduction of the Cornputer
an
rne Statistics
Cr:rricuf trm
SALARIESAND TJAGES
Budset
Expenditures
i triHi!li"i:"i.ffiir=_=i4#:
:::
?i*:"li: #3:;,i.T:lH "f,o_J"-"ii-p.ot_
$r-0,87s
:+..
pre_Baccafaureate
1,0,650
Students (4)
5 , 1 20
Jecretarial
500
TOTAL SALARIESANDwAcEs
$261fIF
EXPENDABLE
EQUIPMENT
AND SUPPLIES
710
c.
T R A V E L ,D o n e s t i c - , 5 0 c o n f e r e n c e p a r t i c i p a n t s
g a v g . 5 0 0 x n i l e6 / p a r t i c
ipa"i @ e+U;,it.-
D.
ttO Otl",, -,1.0._"onf,enence partici.pants
^ + qays
2,000
@ $l-O/day
2,000
OTHERCOSTS
publicity
(confenence)
],
2. Reference Material
3. Key Punch Rentals
$
200
IO0
? rrn
TOTAL OTHERCOSTS
3,420
TOTAL DIRECT COSTS
P
$11,13s.0
I N D I R E C TC o S T S- t + S . 3 t o f A . I a n d 2 , a s
requested
TOTAL COSTS
A.l4ol.,NT0F AWARD- Rounded
6,24s.0
9,751
$46,026
$46,ooo
$46,000.0
',/t*tA./i^
Ertioi
l.-TEris-
Proj ect Director
Controller.
and Chief Fiscal
Officer