PROPOSAL
TO THE NATIONALSCIETJCE
FOUNDATION
CoverPa0e
FOA CONSIOERATIONAY NSF OFGANIZATIONAL UNIT
lltrd.crt€ th. doir lpecilic !.n r.@.
ir. g.ograh, divirio...tc. l
ABE AI]Y FUNOS IIT T}1|S PAOPOSAL EgII\tG Ft€OUESTEO
€LSEWHEFIEIN NS' OF IN ATO''H€R FEOERALAGENCY
lnitructioAalScientific Equipment
Program. ISEP
pBoaFAMaNNouNcEME"tr"oa'"'t t'o* nU;a
Yesu
No
iF Y€S. EXPLAINUttOEBREMAqKS.
cLoSlNGoATE tlF a||Ylr March2, 1979
rr.a,
NANEOF SUSMTTTTNG
OqGANtzATtONtO tl'HtCHAWAROSHOffi
tlope College
AOOaESS
OF OSGANTZAT|ON
ITNcLUOE
ZrFCOOET
Hol1and, ur
49423
EO PAOJECT
A llicrocomputer Laboratoly for Use in Teaching Statistics
5 N E O U E S T EFDR O MN S F
S L O C A LC O N T F I B U T I O N
s1 0 , 3 0 0
STOTAL PFOJECTCO5T5
$1 0 , 3 3 0
:il,-r:Ul:O:)iiitAItON
I
2 years
o E S t n ! o s T A t t T i N 6D A i t
I
PIIPD NA'IE ANO SOCIAL SECURITY NO
Elliot A. Tanis
481-34-8023
s2 0 , 6 3 0
Septenber, 1979
ry-pHoNEt\o---
Ext 3001
I oFFrcE:616_392_St1t
I HoM€:616-396,-2228
PI/ID OE?AATMENT
FI/PO OF6ANIZATION
I'lathematics
Hope College
A o o l T r o N A L P t / P OA N O S S f t '
A O O I T I O N A LP I / P q A N O S S N '
Herbelt L. De shern
A O O I T i O N AP
L t/tO ANOSSN'
A D O I T I O N A LP I / P OA N C S S N '
'sub'k.ion or o.a.r r..uriry nuhb..r irvolu^r.'y..d
wrll no!.tt.d
i^..r..r r.4 or lh. f.lsF anlo'6.rro. ry.r.m..d st.t l.
ININCIPA! INVESTIGATOB/
PFOJEC' OIFECTOA
ruar.r:te,or.,@ r"r,.,
ra;.t
El 1 i o t A . T a n i s
0>
TriLi Profcssor Of l\lathCmiLt j c s , C h o i l r n : r no € l \ l i r t h crlratics Dcpilrtfircnt
AU'HOFIZEO
ro' r^ N.'d. ltowo.r. rh.y.r.h
!h. o.t..i..riont.ritibirrrv
SSN.6rici:.d !nd.' nisF A.tol 1950,.'.6.mt.d.
OTHEh ENOOASEMENT
ORGANIZAIIONAL FEP.
NAI$E {P.or.,g)
r., t'le.1
NABE
Sheldon liettack
"Wtta^/M
SIGNATUAE
De:rn, Lli\,isio s ot_
Natura'l arrd Sorixl Scicrrccs
OAI€
I ' c i ) r ' u i r r y2 6 , 1 1 1 7 9
lProt.. Oi. M..,lvlt.)
February 26, 1979
t9
DETAILEDBUDGET
(1)
(2)
G EqJIPqNT
Each
Total.
+6K RAMl,evel-Il BASIC, TRS-80
l.licfoconputers
$9E8
$9880
?oo
2990
499
4990
10 qxpanslof Irterf,aco
( 3 ) 10 Dtsk Driios
(4)
1 Li]nePrinfer, Tractor F6ed
(s)
QtlickPri+ter
(6)
Piint€r cdmectionCables
(7)
nd.zgz-c{oeras
(8)
1499
499
499
78
99
198
Interfaces
$20,650
NATIONAI.SCIENCEFOUNDATION
UNDERGPADUATE
SCIENTIFIC
EOUIPMENT
PROGRAM
ProjectS!mmary Form
Hope College
r.'funcrr^L'NvEsfl
Ho11and, Michigan
49423
o^ro-
Elliot A. Tani.s
Ncd ^HD .Ncr{EEi'Nc
c-6G
6. 'sr.riorEcr'3rRiN%
+&KoN!,
ssc!^rGtr
rYrc o. 'Nsflror'ox
*cc^L^uFMr.&
BNilRc
i-t-E;
6oc,oic
FT.onsoR
fi
ter Laboratof,y for Use i.n Teaching Statistics
sUM"ARyoF'Ro.ostowo*
A labolatory loon containing ten Radio Shack TRS_80niclocontrure!
systens wj.l1^beused to. inpleDent Laboratoly coulses uhich are ad-iunct
!o Ehree dtttelent statistics coulses at HopeCollege. fhe three courses
are Introductory Statistics for non-science najors, Mathenatical
Statistics and Probability for natherndticsrnajors,-andStatistics for
Scientists,
The conputer laboratory exercisei fox the first two coulses
have already been developed and are being used in nany colleges. The,
exelcises fo! the thild laboratory will be developed under a-CAUSE
grant to HopeCollege.
. The laboratory courses uill be enhancedby the addition of this
because it Hill pernit the conpletion of laboratory experinents
"l::pr"l: the classroon envilonnent
ritthln
under conditions controlled and
supervised by the instructor.
This Bil.l lesult in nore efficielr
use
of both instluctor and student tine and a _nore conducive environne[r
for Iearning statistical
concepts.
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For.c,
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^ssoc,^aE
a 5_YEA6 FERroo
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20
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lsv.L.
NARRATIVE
A.
NEED: THE PRESENT
SITUATIoN
The computet is ?resently
tional
tool in statistics
statistics
being used in several ways as an lnstruc_
classes at Hope Co11ege. An introductory
class with no calculus prerequisite
is offered for students
in the social sci.ences, This o'te semester, three credit-hour
had an average annual enrollment
credit-hour
laboratory
This laboratory utilizes
of statistics
coulse has
of 232 o\tet the past three years. A one_
is offered
as an optional
adjunct
to the coufse,
the cornputer as a tool to aid in the learnlng
through the use of sinulations,
graphi.cal dis?1ays, and
analyses perfoxrned on data sets stored in the conputer.
Unfortunately
less than 20%of the students elect to take the laboratory.
A two-course sequencein Mathenatical Statistics
also offered
senestels.
each year.
It
This course is thlee
is offered prinarity
credit
and probability
is
hours each of two
fot Mathenatics najors at the junior
and senior level and has a calculus prelequisite.
During the past
thxee years this course has had an average enrollnent of 25 studelts
fixst
semester and 19 students second senester.
A one-credit-hour
conputer labotatory is also offered as an option for students enrolled
in this course,
Approxinately one-ha1f of the students elect this
laboratory which seeks to use the conputer as a tool to illustrate
reinforce
the theoretical
concepts in p"obability
and statistics
and
through
extedsive use.of graphics and sinulations,
The students who do not
elect the laboratory xeceive only a nininal
exposure to the computer.
A third
course in statistics,
intended prinarily
for natula1 science
students, is being developed with suppoit fron a National Science
Foundatibn CAUSEgrant.
A version
spring of 1978 with an etroltnent
of this
course was offered
during the
of 15 students. Based on our first
-2exPellence with this
sirdlar
course, l,e plan to iategt:ate
co[puter
laboratory
work,
to that now offered in the two present courses,
into thr5 one-
semester calculus based course,
A suunary of past enrollnenrs in the two present
statistics
and their laboratories is found u Table I.
Detailed
offerings
descriptions of the
courses are found in Appendix B,
Course
1976-77 1917-78 1 9 7 9 - 8 0 Ayerage
Illtroductory Statistics
Intlo
239
227
Stat Laboratory
Math Stat-no lab (falt
230
232
11
10
12
10
9
36
enrollment)
Math Stat-with lab (fal.1 ellrollnett)
19
Tabl.e I
In spite of ?elatively
stable enrollnents in statistics
Hope over the past three years, the total
statistics
courses ar
.nurnber of students enrolled
in
conrputer laboratoxies has ilecreased frorn 70 to 40 (see
Tabte I).
This decrease does not appear to have occuled
because the studedts do not
find the laboratory valuab1e,
On the contrary, student evaluations of
the laboratories conslstently
indicate that the laboratoty has ucreased
the students' u[derstanding of statistical
concepts anal givel then a
valuable experielce with data analysis and interpretion.
students who enroll
in the statistics
for the laboratory
class.
generally
It addition
receive higher grades
No doubt this i.s due in part to the fact that
often the better studedts elect the labofatofy.
The faculty
who teach the laboratories
reasons fo" the enrollmeflt
feel
that one of the lnportant
decrease is the large amount of tine
s?ent by
the students working on the conputei outside of c1ass. The
use of our pre_
sent conputer systen has often been a ftustrating
atory students because of linited
experience for the tabor-
terrninal availability
and slow response tine.
This is the result
of the linitations
of the cuirent Hope College conputer
systen and the large nuruber of students using the collputer for lnsttuctaonal
purposes, Each senester the con?uter is used in courses with
enrotlnents
totaling
nore thall 500.
The college has a Honefvell Signa 6 conputer systen which is shared
by all
acadenic and adninistlative
for general student
without
further
users.
use on canpus.
Only six terninals
are provided
This nulnbe! cannot be increased
enhancernent of the conputer system to acconodate loore users.
our current
t)?ical
blockeachweek, The first
laboratory
for both couxses meets for a two hour
part of each period is spent discussing the
results of the ex?erinents assi.gned during the previous week. (See Appendix
C for sone t)?ical
experiments. ) A new experinent
students can spend the renainder
of the 1ab tine
is then alescribed. The
in pTeparation for the
experinent. Generally there is at nost one telndna1 available for the
gtudents to begin pelforning
Under the resttictions
the elTerinent
on the conputer.
of the present conputing equipnent, nost of
the students nust perforJn the experir0ent sonetine during the week between
laboratories.
available
for assistance and at a tine
discussion,
the students.
teminals
This nust be dorle at tines
This is one of the frustrating
other fxustrations
aspects of the laboratory fo,
are the lack of an adequate nuDber of
time. This proposal is an attenpt
so that a nore ideal
instructiolal
is flot
separated fron the labolarory
altd slow systen response time, xesulting
wasted studelt
B.
ohen the instructor
in a large a[ount of
to inprove this
situation
sequence can be inplemented.
PRoJECTpESCRIPTIoN:THE IMPROVEMENT
PLAN
Based on our past experience, the ideal scenario fot the statistics
laboratories would be for the instructor
techniques for the erperinent
ro presenr tie background and
during the first
part of the two hour
-4-
petiod.
After this plesentatiod,
the students, in teans of 2 o, 3.
should perforn the expe i.nent at a terninal
under the instructorrs
vi.sion. At the eDd of the period, after
the data has been collected,
the instructor
would further
explain
all
any poilts
super_
brought out by the
e)cperirnent.
The proposed equipnent would altow us to establish
laboratoty
classloon where the statistics
a dedicated
conputer laboratory
courses
could be taught. Thj.s classroon would contail ten conputer starlons,
allor{ing u? to 20 students per laboratory c1ass, with two students assigned
to each station.
This woutd al1ow the instructots
to conduct classroon
denonstrations with each pair of students following a step-by-step procedure
on theix
own data,
It would also perrdt
inents during cLass tine
the students to conduct the exper_
and with direction
alld supervision
fTon the
instructor.
An added benefit
graphics abi.lity
printer
g+ahics.
that the proposed equipnent would give i.s inproved
conpared to ou! ptesent system. llle are culrently
(See Appendix C fo! exanples.) The TRS-80 graphics,
though not as high resolution
as son€ systems, does provide adequate
graphics for the purposes of statistics
Laboratory naterials.
graphical displays used in our statistical
with supelinposed probability
illustlations
using
density
behavior of safip1e statistics
experinents include histograns
fuctions,
of confidence intetvals,
The
scattergtans,
€rd graphical
graphical
illustrations
in conpatison wj.th population
of the
paladeters
as sarnple size is varied.
The students vill
also have the ability
oun ?ersonal data sets on a tnj.lidisk
systerd when needed.
to create and naintain
which could then be loaded into
their
the
Each student in the class would purchase a rninidisk
which wou-tdthen be Lrsedfor storage of any data thac the student mlgh!
wish to use ilt the class experirnents.
D . EQUIPMENT
1. The Equipnent Request
Each station will
consist of a TRS-80 computer vith
BASIC and 16K of nenory.
This is a nininal
the prograns in our software packhge,
and an expaosion ilterface
sion intetface
configuation
In addition,
are lequested for
Level II
for runnlng
one minidisk
each station,
drj.ve
The expan-
is necessary for use of disks- The disk drive is
requested because the loading of prograns and data by cassette rape 1s
very slow on the TRS-80 systen. The length of tirne required by
progran and data loads would be inconpatible with the goal of efficient
use of class ti.me. IIl additiol,
realisti.c
it
would discourage the use of large,
data sets.
In additio[,
two of the systerns will
addition of RS232coNmnication interface
and printefs.
This would peudt
be fuxther
enhanced by the
boards, tetephooe interfaces,
ProfessoE Tanis and Dershen to convert
our present prograns to the TRS-80 systen and to develop ner software.
The conmunications equipnent will
pernit
prograns fron the Hope College centlal
The printers
developtlelt
will
the t"ansfor
of data and
conputer to the TRS-80 and back.
be used to obtain proglan 1istilgs
to assist i.n the
and debugging of plogra$s and for cornputer text
editing
of laboratory naterials.
The TRS-80 conputer system has been used extensively
Dersheb for over a yea! alld a hal.f in various
including
by ptofessox
instructional
heavy usage by elementary school children.
Based on his
experience, the TRS-80 is a sufficiently
ngged and leliable
for use in the statistics
In addition.
fu11y inplenented
tlcs
labotatories.
about 20% of his experinents
applications,
nachine
he has success-
in the elenneltaly sralls-
lab on a TRS-80 systen to test the feasibility
of this project.
-6Becauseof the versatility
to utilize
and ruggedness of the TRS_g0,we erpect
this new equipnent in several other ongoirlg coulses.
exanple, our basic nathenatics course fot liberal
about 1/3 of its
tine
For
arts students devotes
to the conpute! and BASIC progranming, Another
exaople is the taboratory
fot
elenentary
education students which
currently uses petsonally ohred TRS-80's for denonstration lulDoses.
2.
The Equipneot on Hard
Hope College owns a Honeywell Sigrna 6 conputer with 96K of
nenory and 24 comunication
di.sk storage units
ports.
Also i[cluded
and orle tape drive.
ale six 24! megabyte
Terndnals available
for
student use include 2 Decwriters, I Teleray CRT, and .3 Teletne
KRS33 terninals.
The use of additional
nenory of the central
processing unit
disk storage. In addition,
it
terininals is litrdted by the
and the size and speed of cuxrent
is irnpossible under present cilcumstances
to obtain exclusive use of a bank of te rinals fo! a give[ class or
labotatory.
Hope College al.!o ol'ns one Tektronix 4051 graphic systen which
could be an effective
Ou! use of this
tool fo! use in the statistics
equipment is limited
to classroon denonstrations
because only one systen is avaitable.
The Tektronix 4051 is too
expensive foT us to purchass a sufficient
to have haltds-on usage durilg
3.
labo"atories,
quantity
to a11ow students
class tine.
Equipnent Maintenance
Hope College wi]l
proyide proper
equipnent r,rith a tirne and naterial
Shack store.
naintenance of the purchased
agteenent through the local
Radio
-7D.
PERSONNEL
l.
Faculty Expertise
The experierce
of professots
conputer-based statistics
listing
Dershen and Tanis in the area of
instruction
is extetsive.
experiences are foucl
lertinent
Curriculum vlEae
i"n Appendix A.
With support fron a grant by the Office
of Conputing Activities
of NSF, Professors Tanis and Dershen wxote a colputer
Package fof, statistics
distlibuted
instruction.
software
This package is culrently
by CoNDUIT, Borh are authors of laboratory
computef,-based statj.stics
laboratories
beilg
DaDuals for
and have authored or detivered
Dany papels on the use of the conputer in teaching statistics.
Plofessor
Dershem is Selies Bditor
in statistics
for CONDUIT,
Both Dersher! arrd Tanis a!.e orf,Dols of Radio Shack TRS-8O conDure,
systems and havo experience in the use of such a systeD.
2,
Infornation
on iurrent
or proposod projects
Professor Dershen is servilg
as director
Modular Approach to the Introductory
of the pt.oject,
Coulse in Conputer Sciencer,
funded by tho Locaf. Coulse Ir[ptovenent progranl of the National
FoundatioD. fhis project Bill
Professor Tanis uill
National
statistics
related
involves
be a participant
in a p oject
the design and j.nplenentation
course for natural
to the pro?osed project
science students.
fatt
of 1979.
fundod by a
His
of a ono-senester
This gork is closely
since the requested equilnent
would be used to provide a conputer laboratory
Professor Tanis will
Science
be conpLeted in August, 1979.
Science Foundatioo CAUSBgrant to Hope College.
palticipation
r'A
be working on this
project
for this
new course.
during the su$rer and
E.
EVALUATION
The project will
be evaluated by the participating
studelts enrolled i.n the laboratories,
and faculty
faculty,
the
teaching statistics
coufses at other institutions.
olle iEportant
laboratories
neasu?e of the success of this
will
be the trend in enrollnent
the next three years.
new approach to the
in the laboratories
A high student opinion of.tbe
is best measured by the way that
possible future enrollges.
opinion influences
over
value of a class
students who are
Fomal student evaluations will
also be used
and coftpaled with those which have been received wheo the
?resent approach
to the laboratory has been used.
The inst"uctors
by conparinS it
tine,
instj.tutions
at regional
Softrare
evaluate the new approach
j.n the ploductive
uith
which the studonts operate the
to learn statistical
concepts and practices.
the evaluation of this prbject by colleagues at other
wiII
be accotrplished by ?resenting
and natio[al
developed will.
our approach in papers
conferences and publishing
also be nade available
lesults
be a need for software that nakes efficient
purposes.
in journals.
fo, use by others.
As the nunber'of TRS-80is in education inc"eases rapidly,
educational
use of
in the percoived and neasureal learning
and in the facitity
equipnent and use it
Finally,
will
to the previ.ous situation
facuLty and studelt
taking place,
of the laboratory
use of this
there wiII
conputer for
-1APPENDIX
A
Staff Vitae
I.
Director - Elliot
A. Tanis
Educa!ion:
1.1.
Y:S:
vn.u.
Central Co11ege, pe11a, Iowa, 1956
University of lowa, 1960 (Maihernatics.l
Univelsity of Iowa, 1963 fMathenatics.)
T h e s i s : " L i n e a r F o n n si n t h e O r d e r S r ; t i s t i c s
fron an Exponential Distribution,'.
Professional ExDerience:
Assistant Priofessor of Mathenatics, University of Nebraska.
1963_65.
Menber of the faculty, Hope Cotlege, 1965_present
Currently professor of Mathenatics and
Chai.xnan of the Departnent of Mathenatics.
Associate Director, NSF SurnnerIlstitute
for Advancedplacenent
Teachers of Mathernatics, Hope Co1lege, 1967, 1968.
Director, NSF Sunner Instltute for Advancedplacenent Teachers
of
Mathenatj.cs, Hope College, 1969,
rilntroduction of
Director, A project:
the Conputer in the Statistics
Curriculunt', under the Office of Conputing Activities,
NSF,
1971-73, with H. Dershem.
Professionat Affiliations
:
Nlathenatical Associatiol of Arnetrca
tunerican Mathenatical Society
Institute of Mathenatical Statistlcs
Anerican Statistical Associatior
Society of Signa Xi
Pi tr4uEpsilor
Releva[t Publications:
rrTheoryof Probability and
Statistics Illustraled by lhe Conpurer..,
Proceedines of the I972 confereece on Cornptrter!in tl..e lJndergraduate
eiiilcut-al-Jun-ne-T-s7r--
"A Cornputer Laboratory for Mathenatical Probability and Statistics,'.
Proceedings of a Fourth Conference on Computers in the Undergraduate
-
eE;'icrtff-.
Jun-e. ls7::-
'rMathenatic.al Probability
and S t a t i s t i c s C o n p u t e r L a b o r a t o r y " ,
International Journal of Mathenatical Education in Science and
r e c n n o . l o g yA
J pr11, 1974,
El1iot A. Tanis cont. . .
Probabilitl and Srati st i ca1 Jn-[erence
with Robert V. HogC, tg77;-Fcmrf.tan pub-tisn-Lng
Conpany.
t"oo":::,"t
f?" PI"b?9.1=Ii:I
and s.t_alist:calr:rference
, by CONDUIT,
rel0, TflY"1,
crrstributed
EhemIt;;;lt
;F-lowa.
"o a"ll:l:lll::O
Laboratory.
for MathenaticalStatistics and probability,,,
an.!ig!!L conferenceon conputers in the Undergraduate
f:*sss9++9.9!
LUTrlCUla,
June, lg77,
Relevant Papers plesented:
rrTheory of Probability
and Statistics Illustrated by the Conpute!,,,
1972 Conference on Computers in the Undergraduate Curri'cu1a,
AtlantaJ ceorgiar June, 1972.
"A Conputer Laboratory for Mathenatical probabitity and Statistics,,,
Fourth Conference on Conputers in the Uldergr;duate Curricula,
L t a r e n o n tr U a l t i o r n i a , J u n e , I 9 7 3 ,
"Mathematical PTobability and Statistics Computer Labolatory,,,
FiTst British Conference on Conputers Ln Uigner gaucation, Lancaster,
England,Apri1, 1974.
"A Conputer-Based. Laboratory for Mathernatical Statistics and probabitity,,,
NAToAdvancedStudy Institute on Conputet_BasedScience Insrruc!1on,
Universite de Louvain, Be]gium, July, 1976.
"A Conputer-BasedLaboratory for Matherlatical Statistics and probability,r,
Annual neeting of the Anelican Mathex0aticalSociety, St. Louts,
Missouri, Januaxy 1977.
ItDistribution
Theory Illustrated EnDirically,'.
Annualneeting of the Anerican Statistlcal
T11inois, August, 1977.
Association, Chicago,
Based l,aboratory for. Mathenatical Statistics and probabilityr,,
"A Cotn?ut-.rMichigan Association of CotnputerUsers for Learring, SecondAnnual
Convention, Grand Rapids, Michigan, March, 1978.
II.
Herbert L. Dexshen
Education
B .S .
I v l .S ,
Ph.D.
lcurn laude) ljnivexsity of Dayton, 1965 (Mathernatics)
Purdue University,. 1967 (CornputerScience)
Purdue University, 1969 (Conputer' Scieltce)
Professional Experience
Menber.of the faculty, Hope Co11ege, 1969-present.
Currently Assoeiate Professor of Mathamatics and Conputer Science anil
Chairnan of the Departnent of Computer Science,
-3Herbe"t L, Dershen cont. , .
Participant, A project:
"rntr.oduction of the conputer in the statistics
Curriculunr', Supported by The Office of Coi,p"ti"l'
n.fivltr
es, NSF,
1 9 7 1 - 7 9 ,w i t h E . T a n i s
project COMPUTe,
Dartnouth Cotlege, 1974,
Palticipant,
Metnber, CoNDUITNational
Statistics
Director,
Mathenatics Advisoly Connittee,
1974_p_resenE.
Seties Editor, CONDUIT,1977-presentA Pxoject:
,'A Modular Approach
to the Introductory
Course
in Con?uterSci.ence,,supporiuaty Lo""r C.".r" irproulr"nt
Progran, NSF, 1978_79.
Professiotal
Affitiations
Mathenatica.l Association of Anerica
Association for Conputing Machr.nery
]EEE LollpuleT Society
Society of Data Educators
Society of Sigra Xi
Pi trtuEpsilon
Relevant Publications
'rA Course on conrputilg
and statistics for social scie[ce
-in-ti"-Jna""gr"au.t"
students,,,
,
Proceedings of the 1972 Conference on Corputer"
Curriculh, Atlanta, Georgia, I972, pp. s2i-SZB.
trExercise Manual for
a Corputer-AugnentedApplied Statistics
C o n P r e s s ,I n c . , 1 9 7 9 .
rrA TeI atilnship. between
approxination theory and statistical
r,r Mu Epsllon Journat, 6, 2(Spring, 1974), pp. 69_74,
Course,,,
neasurenents,t,
rrFacto! Garnerr
Personal Conputing, 2,6(June, 1978), pp. 44_49.
rrlntroducing Elenentary
School Chj.ldren to the ConDuterr.
Calculator/Conputels Magazine, 2, 6 (Septenber/6ctoter, f sZe;,
PP. 69-71, with J. Whittle
I'ConFuters in Teaching Mathenatics",
Coryruters in Undergraduate Teachingl tgTT CONDUITState of the Art
Reports in Selected Disciplines, CONDUIT,197g, with D. Mcl,aughtin,
A. Ziebur, and D. Snith.
'rExperinents in Statistics
ln preParatlon.
with BASIC prograns:
A Laboratory Manual,,,
-1-
A.PPENDIX
B
Catalog descriptions of our current statistics
courses
210. INTR0DUCToRY
STATISTICS- A general introduction
statistics
for students najoring it
the binonial
to the area of
other depattments. Includes study of
aIId oofllla] distributions
with applications
of estidration
and testing of hypotheses, non-paranetric nethods, regression and
correlation,
and analysis of variance.
212. LABoRAToRY
FoR INTRoDUCToRY
STATISTICS- The conputer is used as a
tool to aid in the learning and understandilg of statistics.
given in the use of statistical
Co-requisite,
Experience
analysis packages. pxerequisite or
Mathenatics 210.
361. I4ATHEMATICAL
PROBABILITYAND STATISTICSI - Concepts of probability,
probability
functions,
as relative
frequency, randornvariables,
cr.mulative distai.bution
functions,
mean, variance, confidence intervals.
three hours credit.
optional
Laboratory,
Prerequisite:
density
tnathematicaL expectation,
Lecture, thlee hours per vreek for
Mathenatics 235 - Calculus II1.
two hours per week for an additional
hour credit.
Mathenatics (Cohputer Science) 120 - Introduction to
q^ i an^d
a^ffir!+or
362.
Prerequisitel
probability
MATHEMATICAL
PRoBABILITYAND STATISTICSII
- Continuation
of
Mathenatics 361 ernphasizing statistics,
Estination,
h)?otheses, reglession and corlelation,
analysis of vatiance, Lecture,
thxee hours per week for thxee hours credit.
optional
laboratory,
q^i
prerequisite:
tl^ro hours per week for an additional
Mathenatics 361.
hour credit.
Mathenatics (Conputer Science) 120 - Iltroductlon
Prerequisite:
li^!ffirlro'
testing of statistical
a--d
to
-1-
APPEM]X C
In this
statistics
Iaboratory.
statistics
appeldix we give the table of contents for the introductory
laboratory
along with one set of experinents
We also give the table of contelts
for this
for the nathernatlcal.
laboratory, one problen for this laboratory along with the
solution for this problen.
-2-
'lable
Part l:
of Conrcnts
Conputcrlxcrcises
llow to Use the Conputcr Excrcises
Ijescription of the Conputer Exercises
t . The Law of Aver.ages
2 . Sumof Pairs of Dice.
S o m e . R u l e s o f l r o u i r r i f i t:i : : : : : : : : : : : : : : : : : lt02
4 . Londrtional Probability
1,4
5.
ba)'es formula.
6 . Penrutations
Co^rrln"iioni: . - - ",.ta
7 . computations
Gb;;;-i;-t;;ui"iioui
"f
- A Card Game
8 . Conputer Sinulation
9 . C o m p u t Se ir m u l a t i o- nA C a r n i v aGl a n e
t 0 . I;reqticncyDistribut.ion - Dicc
lo
l7
""j
io",ui"o.ionr. . . l 8
20
2I
23
- ii".o"L's"ti
1 1 . r,rcqriencyoist.iuuiion
: : : . : : : : : : . 24
12.
2S
Mean andStandard Deviation of Grouped Data . . . . . . : . . 2 7
14.
lgsting a Rando:nNunber Generator
28
1 5 . The Median.
16, P e r c e n t i l e s . . . : : : : : : '
3l
1 7 . LneDycrlevs inequatlty1 8 , Probrbility Distributions
55
1 9 . The Binonial Distribution
2 0 . Binonial Probability.
56
'l
2 r . 'lhe
hc Norl|rall)istribution
38
22.
StanclardNonnal ljistribution.
. . .
59
2 3 . Nonnal Approximation to tlte Binonlial.
4I
Nonml Approxination to the Binomial - llistosrams
42
RandomNrunbcrCencrator
:........
43
2 6 . IlandlmSampling fron a Probability Distr.ibution
45
2 7 . RandonSanrpling fr.on Data Scts.
2 8 . SdlnpLingnistribution of the l\tean,
.
2 9 . U n b i a s c dl : s t i m a t c s . , . . .
49
5 0 . A S t i l t i s t i c i lI S u l ) r o u t i c .
5I
<l
Ccncratc Statistical 'l lblcs
52
3 2 . r\n Alphabctical FrequcncyDistr.ibution,
11
I)ririi,rd.
t).
".
.........
c^r
3 4 . Confidcnce lntcrv|ls,
3 5 . Studcntrs t Distribrrtion.
3 6 - I )ctc lrninirt io| ol. SarU)lcSj.:e.
l : s l i n r i l t i o no f n p r o l ) o r t i o n .
38- lcst ing ol' ),l()thcscs
'l
i!).
cst ing ll),1)othcscsfor. L i v c l ) i l t i r .
'li.st
40,
i r ) g t l r c l ) i l - l c r . cc ( . ol' 'l\ro i\L'ilns
58
59
61
t,2
65
($
Table of Contents (continucd)
ConputerExercises (continucd)
Testing a proportion.
42.
67
68
Correlation
69
70
7L
Regressionand StandarclErroi of
4 5 . Testing the Central Li.nit TheoremE s t i m a t e ,
4 6 . Iesttng a RandomNurnberGeneralor
ContingencyTables.
4 8 . Tcsting a ltedian.
4 9 . Testing the Difference of Two l.'ledians
Part 2 :
7S
Subprogr.uns.
78
Description of the Subprograns
1 . BINOI'I
2 . BMlo
colt
c$ts.
4.
5.
6.
7,
8.
9.
10.
11.
12.
13.
14.
15.
16.
77.
18.
19.
20.
21.
22.
p1
MNIN
CORRE
DMI'T.
FCTSQ
82
83
84
85
86
86
FI,iP.
NRI'lL
83
88
89
90
9t
91
92
93
93
94
GU\t{.
HISTl
ITOSS
N0Rltl
tEK
PER,\'.
PRC}II
PRF
PRI
PIi:
R.\\ .
2 5 . S.-$IPL
2 6 . sL'.,u
2 7 . slt\sv
2 8 . SUPIIR
2 9 . IJR\
l):lrt
79
80
81
3 :
Ilata : i c t s .
I)cscr il'i irrt of
.
.
-
95
96
97
97
98
.100
.10I
.101
. .l0i
105
-4Laborator.y 4
The purpose of this laboratory is to leam holr to generate
!g:!g:g:
frequency distiibutions
arld histog"ans on the computer, to ve1:ify
Chebyshevrs Theoren, and to use the cornputer prograns io test fot nornality.
Experinents:
I A data set ca11ed STUDENT
is stored in the conputeris storage. Thexe
are two varciables in this data set, HS6PAand SATI, and 150 s;irples.
Use
the procedutes fron Laboratoties 2 and 3 to retrieve and pri4t neasures
of central tendency and dispersion for this alata set.
2. Generate a frequency distribution
of data set STUDENT.
analhistogram for both variables
3.
_Usethe progran FREQto verify Chebyshev's Theoren for k = 1.5, z, 5,
and 10 with either var:iable of data set STUDENT.
4. C"eate and save a data set of your ohrr choosing, It
least 2 variables and 20 sanples
should have ar
5. For one of the variables of the data set you entered in lxperinent 4,
use FREQto deternine what proportion of sanple values are within one,
two, and three standard deviations of the ne;n.
Analysis:
1. In Experiment 2, how can you use the results of Experinent t to
deternine the linits for the flequency classes?
2.
Sunmarize the results of Experinent g in the table below:
NyJn!9r of sanple values
Lower bound predicted
:k
k staldard deviations
by Chebyshevls Theorem
-wlthin
.1.'
2
5
l0
3,
Describe the data set you created in Experirnent 4.
Population fron which sanples were taken:
Variables in the data set:
4.
Sumnarize the results of Experiment 5 in the table belowi
PToportion of sample values
Expected proportion
k
within k standard deviations
nomal disttibution
1
2
3
Do these lesults
indicale that your var-iabie might be norlltaI?
for
LABOMTORYMANI'ALFOR
PROBABILIfi ANDSTATISTICALINFERENCE
CONTENTS
Chapter I
.
PROMBILITY
l.L
RandomNr'rlber Generators
1.2
probability
1.3
properties of probability
1.4
pemutations, Conbinations,
Sanpling With and.
Without Replacenent
1.5
as Relative Frequency
H)?ergeonetric probabilities,
Iyithout Replace4en!
1.5
Cond.itionat Frobability
1.7
Bayes' ForruLa
1.8
Independent Events
Chapter 2
I
4 '
q
t2
Sanpting l,/iih al1J
l<
20
t7,
DISTRIBUTIONS
OF lI.tE DISCRETETypE
2.1
Probability
2.2
ltathenatical
2.3
The Mean, Valiance, alrd Ske$ness
2.4
Tt.e Mouent-Generating Function
2.5
Bernoul.li Tlials
and the BinoniaL Distribution
56
2.6
Geonetric and Negative Billorrial DistTibutions
'Ih.e poisson
Distribution
40
2.7
chapter 3
Deusity Functiols
and Distribution
Functrons
E4,ectation
44
BVPIRICALDISTRIBUTIoNS
3.1
Enpirical Distribution
3.2
Histog:.ans and Ogives
3.3
The lvleanand the Variance of a Sa.nple
3.4
Sirnulating RandonSarll'les fron Disctete Distributions
Function
48
s1
54
-6-
Chaptcr 4
DISTRIBUTIONS
OF T}IE CONTINUOUS
TYPE
4 . 1 Randon Variables of the Continuous
Type
60
4 . 2 The Unifom Distribution
.
62
4 . 3 The Exponential Distribution
4 . 4 The Gaura and Chi-square Distlibutions
4 , 5 Ilt'e NorrEl DistlibutioR
66
68
7l
4 . 6 Mixed Distributions
Chapter 5
BASICSMPLINGDISTRBUTIONTHEORY
Distlibutions
of FunctLonsof Randold
Valiables
Suns of IndependentRandom
Variables
The Central LiEit Theoren
diL
Approxlnations for Disc"ete Distributioru
order Statlstics
Chapte! 6
79
84
E7
DISTRIBUTION-FREE
CONFIDENCE
IMTERVALS
6 . 1 Confidence Intewals
Percenti Ies
o . z Confidence Intervals
M6ans
94
Confidence Intewals for Percentages
Sanple Size
Chapter 7
ESTIMATIONIIITIT NORMAL
MODEI,S
I'laxinuE Likelihood
Estiration
101
CoDfidence Intervals
for Means Given Krolrn Variances
r04
gouf,idence Intervals
for Variances
105
Confidence Intervals
for rlteans
I11
Point Esti8ation
114
7 , 6 Functions of para,reters
t l 7
Regression
Chaptcr 8
TESTSOF STATISTICAL HYPOTTIESES\
sone Exanples aIld DefiDitions
tltt
ll9
8.2
Altelnative lry?otheses
8.3
Tests of Variances
8.4
The pol{er Function
t2t
723
B.S- Binonial Tests for percentiles,
t30
8.6
The Mlcoxon Test
8.7
Two Sanple Distribution_Free
8.8
Run Test and. Test for Randonness
8.9
Kolmogorov-srdirnov Coodness
Tests
of Fit Test
LULTMRIATEDISTRIBUTIONS
ChapterI
9.1
Ituttivariate
9.2
The Coirelation Coeificient
9..i
Conditional
9.4
lfultiyariate
9.S
The Bivariate
9.6
Sanpling fron Bivariare
9,7
The Sanple Correlation
chapte! 10
10.1
t32
Distributions
of the Disclete T)?e
746
Distributions
148
Distlibutions
of, the Continuous Type
Distributions
Coefficient
158
o{I-SQUARETESTSoF MODELS
10.2 Testing probabilistic
159
}rodels
r62
10.3 Additional Models
A Test of the Equality
of fwo l,tultinooial
10.5 Contingency Tables
Chapter t1
l2-l
168
770
11.2 Tests of the Equality of
lleans
Two_FactorAnalysis of Variance
Chapter 12
Distributions
ANALYSISOF VARIA]ICE
11.1 A Chi_square Deconpositiod .Iheoren
1I.3
ts2
Nomal Distribution
The Basic Chi_Square Statistic
10.4
744
TRANSFORi{ATIONS
{JF RANDOII
VARIABLES
The Cauchyand Beta Distributions
7''r
t72
t74
-8-
4.2-6.
Let U and V be independent ranalon variables
distributions
dist"ibution.
(a)
Showenpirically
In particulat
geterate
that lll= U+Vhas
the p.d.f.
a relative
g(kJ = 1 - lw - fl,
Use the subroutide OGIVE to plot
curve with the distxibutioD
firnction
a txlangutat
500 paixs of ranalon nimbets-
Use the sub"outine RFHPFto plot
histogra.nwith
(b)
U(0,1).
with uniforin
frequency
O < w < 2, superinposed..
a reLative
frequency ogive
of W suDerinDosed.
-9-
?t2
. P R O A L E f l{ .
?_6.
suBpR6GR^h.
: lE:jii,'ii
N
. e u r c r r ou
r is: i3i ;5' ;.;3; ;.;"r1' t"i l:,,:IE: 'ir: o
i."
^. a srarEi'ENr
FUNCTION
G(h)
;t;ril-aBs(H-rrl
ENO
.
O E FI N E T H E O I S T R I B U T I O N
FUNCTIEN
A S A F U N C T ! S NS U S P R E G R A H .
F U N CI J O N D F t W t
I F t r . L E . 1' ] - D F -
DF ! 1r RETURN
.
tct
-
.!tt+t7t/?.;
R€TURN
dt1ttz/2.
. 0IxENSI6N k tO HOLO
TH
: : ii;!p:_;l;,;;,t;h:,_'3i^i:g.i?.i?yi'ill.i,"3
No8s,
ao)
:iiEiiii-.1,3;or,
. . G€NERAfE
5 o o € B S E R V A I I E N6sF T H E
s U H o F I I , I oU t o , I } v A R I A S L E S ,
D 0 1 O , < : 1 ,S O o
U r R A N tI )
v ! R A N ti I
x(K, ' U + V
1 O C O NT I N U E
pDF
i : iiii:iii:i:il";l,i'i:H.|3;,i':JFi:^t,irrHHrHE
ty"!r;"!,.:i:::s;::::,.1:ir_ii;
: i iijj:i!:lt?x
0E a0 NINT,lOrAOrtO
C A L L _ R F H PI Ft , N I N t , O . O , a .
O , t . e , SO O ,w , N SS S ,G I
w RI I E { 1 0 8 , 8 0 0I
8 0 0 F 8 R F A T t t o ' , 1 0 x , ' s u He F
T , { Eu ( 0 , ! ) R A N o € Jv ,at R r r a | ' s r r
c A L L e c I v E { 1 , N l N T , O , O ,2 . 0 ;
5 o o ,d , o F )
r R l T E i 1 0 8 , 8 0 5r
8 0 5 F e R F A tTr O ' , t O : , , 6 GJ V E
cuRvEFBR tHE sut' sF T11o
uro,1)
xBLEsrr
2 O C € N TI N U E
STeP
€N0
RAi'IOOI' VAR JA
- l0-
?63
6 U T P U TF O R P R E E L E HI . 2 . 6 .
1r2O0 r
l'152 r
1.10{ }
1.056 r
+ ++ + + x
t.004 |
+ + + +X+ X
,960 r
++XX++XX
r 912 r
+ X+ + + ++ + + X+ +
r 864 +
r 816 +
X X + + ++ + + ++ + X X
.768 +
X ++++++++++++X
t72Q +
XX +++++i++++++ XX
+X++++++++++++++++ X
.67? *
r 6?1 4
XX+++++++++++++++++ XX
.576 *
X + + + ++ ++ ++ + + ++ ++ + + ++ + i + + + X ++ ++ +
1528 +
X ++++++++++++++++++++t++++Xr+++
+ x x + + + + ++ + + + t + + + + ++ + r + + + + t + + + + + + x x + +
.480 |
r432 r
X+++++++++++++++{+++++++++++++++++X+
r384 r
XX+++++++++++++++i+++++++++++++++++++XX+++++
r336 l
X +++++++++++++++++++++++++++++++++++++X++++
++++++++++++ia++++++++++++++++++++++++xx++
xx
.?88 .r
x+.t++i+++.|++++++++++++++++++.rr++++++.}+++++++++x+
.210 +
.19a a
X+++++i++++++++++++++++.|'+++++++tr+++++++r++++++++X
i 144 r+++XX+++++++++++++++++++++++++++++++++++++++++++++++++XX
. 0 9 6 + + t X + + + + + + ++ + + + + + + + + ' r + + + + + + + ++ + + + + ++ + + + + + + + + + + + + ++ + + + + + + + X + + +
. O{ 8 } + X + + + + + + + + + + + t + + } + + + + + + + + + + + + + + + + + + + + +f + + + + + + + + } + + + + + t + + + X +f
. ooo Ix+rrrIi.i+++tr*li++I,rr*i.ltI+++++ir++IrrI$++rrI+*+*+Il++{tI++r+XJ
-r00
r80
1.60
2.00
1.20
r4O
'
57
38
49
100
13
85
57
tl
66
2b
SUIl OF THA U(0,1I
RANDgtV
" IA R t A S L E S
.t'-'"
NATIONALSCIENCE
WASHINGTON,
D. C.
f-r.,rre
r:E it\ I l:
ATIOM -''i i/ ir rr
-li\)"
S I P2 0 1 3 1 3
sEP14 rg79
PIESr:r!':r"-''-F
GRANTNO.
PROPOSALNO
sER-7914334
sER-7914334
DR GORDONVAN WYLEN
HOLLANDMI 49423
HEREBYAWARDS A GFANT OF
THE NATIONALSCIENCEFOUNDATION
S10,315 TO HOPECOLLEGEFOR SUPPORTOF THE PROJECT
ABOVE.
IN THE PROPOSALREFEFENCED
DESCRIBED
OF ELLIOTA TANIS,
THIS PROJECT,UNDEFTHE DIRECTION
IS ENTITLED:
OF IV]ATHEMATICS,
DEPARTMENT
'A MICBOCOMPUTEB
FOR USE IN TEACHINGSTATISTICS,'
LABORATOBY
OCTOBER1, 1979 AND EXPIRES
THIS AWABO IS EFFECTIVE
PEFIODIS
MARCH3I, 1982, A 6 MONTHUNFUNDEDFLEXIBILITY
INCLUDEDIN THIS AWAFD.
THIS GBANTIS AWARDED PURSUANTTO THE AUTHORITYOF THE
ACT OF 1950 (42 U.S.C.1861 ET
NATIONALSCIENCEFOUNDATION
SEO.)AND IS SUBJECTTO THE FOLLOWINGTERMSAND CONDITIONS:
(REV.OCT/78) AND SE
FL 118 GBANTGENEFALCONDITIONS
THAT THE GRANTEEWILL SHAREIN THE
IT IS UNDERSTOOO
COSTSOF THE PROJECTIN THE AMOUNTOF AT LEAST 50% OF
TOTAL PROJECTCOSTS.
ON WHICH
THE BUDGETINDICATESTHE AMOUNTS.BY CATEGOBIES,
NSF HAS BASED ITS SUPPORI
THE COGNIZANTNSF PROGRAMOFFICIALFORTHIS GRANTIS
JOHN MACCINII2OA 282-7033. THE COGNIZANTNSF GFANTS
OFFICIALIS KARENL SANDBERG(202) 632-5940.
YOURS,
SINCERELY
ENCLOSURES
(uo" Q./"rt^'-
liill,"'lil3;'
I|*o,f"E,ff"klg"c.ENEWS
2 0 ] 0 / H o m e( :6 1 6 ) 6 ] 72 3 9 2
VaiRaa|teHaIR.om]04/TomRenn.r'oilecl$ol]niormJtionseilic.5/oifice:(616)]92.5111,ext
O F F I C EO f I N F O R M A I I O NS E R V I C E S
october 1, 1,979,
lOR IMMEDIAT! REITASE
l41ch. -- Eope College has been a!.a!ded a 8latlt fro!
IIOT.LAND,
Scleoce Foundatlott (NSf) for the establlshDent
Natlooal
the
of a dLclocoBPule!
laboratory.
lhe laboratoty,
systeos along ltlth
coaelgtj.ng of 10 dlcrocofiPuter
supportlng
equlpnent, w111 cost. 920'630.
contllbure
ooe-half
sclence FoundatLqo wlIl
the NatLo[al
of !hL6 asount alld UoPe College the leda{ndel '
fhe project
will
be dLlected by D!. Eluot
departDent of, loathenatlcs antl D!. Ilerbert
TanLst chaLltoan of the
Dersheo, chalman of the depqrtaelt
of conputef Sclence.
oEe of the ,rse" of these cotlputels !{111 be to lrProve la6oratarf
experLoents 1I! dtatlstlcs
support fron an eerlier
of that grant,
a[il statlstlcal
?rof.
courses,
Tanis has publl.€hed a lahoratory
Lnference and Ptof.
new equipoent,
oiclocoEputerg)
danual fo! Probablliry
course.
Tl1ey plad! rtrlth the addLtLoD of
conQute! syBte4!6 to olcro_
w111 glve llope studeats exPosule to the c4PabLlltLes of,
to edhaDce ilasslool!
in6tructioo
ln a valietl
provide research equipneot for conputef, sciedce r0ajo!6.
facslty
As a letu1t
Der6helr has Publlshed an exerclse daoual for
to adaPt this ogrk ilone otr lalge
The labolatotT
of laork begtin lr'lth
NS? graat dfarded to Eo?e CoUege in 1971.
codputer-augEented applled statistl.cs
this
th15 ls a cootlauatl,afl
idenber \ri11 have the opportunity
of coulses alrd to
Every lloPe student and
to galn exPerience ld the lse of lLcro*
coEputers tbrouth
this
labolatory.
lhe College ha6 beed actlve
itl Provldlng
the nolknd
?lof.
dicrocoquters
fo!
cor@udty.
Tad1s sdd D,erEheo, have useil ol'cfocqoputers
Johd Whl.ttle,
l[tth
eleroentery
the quest plogren erd ld clasarooo deoon8tlatlon6.
elclocoqutela
last
foi
19 locel
professofi?
aloEg !.lth
school
chlldren
1n
A ltorkdhop ln the u6e of
eleEeotary ald secoodary dchool teachers wad offeled
su@€! by grofes€ors $hlttle
CoUege r.1ll
educatloE ill the use of,
and ller€heD.
with thlE nev eqdgoeat
be sble to cootlnu€ ard q<psad these actlvl't1es
th€
for elea dtudeDtg
and teacheis.
79-29
NATIONALSCIENCE
WASHINGTON,
D. C.
sEP14 1979
GBANTNO,
NO,
PROPOSAL
Pnfs||1.'rfi
HOit: ,-
sER-7914334
sER-7914334
DR GOFDONVAN WYLEN
HOPECOLLEGE
HOLLANDMI 49423
HEREBYAWARDS A GRAM OF
THE NATIONALSCIENCEFOUNDATION
S10,315 TO HOPECOLLEGEFORSUPPORTOF THE PROJECT
ABOVE.
IN THE PROPOSALREFERENCED
DESCRIBED
OF ELLIOTA TANIS,
THIS PROJECT,UNDERTHE DIRECTION
IS ENTITLED:
OF MATHEMATICS,
DEPARTMENT
FOB USE IN TEACHINGSTATISTICS."
"A MICBOCOMPUTER
LABORATORY
OCTOBER1, 1979 AND EXPIRES
THIS AWARD IS EFFECTIVE
PERIODIS
FLEXIBILITY
MARCH31, 1982, A 6 MONTHUNFUNDED
INCLUDEDIN THIS AWARD.
OF THE
THIS GRANTIS AWARDEDPURSUANTTO THE AUTHORITY
ACT OF 1950 (42 U.S.C,186I ET
NATIONALSCIENCEFOUNDATION
TERMSAND CONDITIONS:
SEO,)AND IS SUBJECTTO THE FOLLOWING
{REV,OCT/78) AND SE
FL I18 GRANTGENERALCONDITIONS
THAT THE GRANTEEWILL SHAREIN THE
IT IS UNDERSTOOD
COSTSOF THE PROJECTIN THE AMOUNTOF AT LEAST50% OF
TOTALPFOJECTCOSTS,
ON WHICH
THE AMOUNTS,BY CATEGORIES,
THE BUDGETINDICATES
BASED
ITS
SUPPORT.
NSF HAS
THE COGNIZANTNSF PROGRAMOFFICIALFORTHIS GRANTIS
JOHN MACCINII2O2I 292-7033. THE COGNIZANTNSF GRANTS
{202) 632-5940,
OFFICIALIS KARENL SANOBERG
YOURS,
SINCERELY
ENCLOSURES
Sept€nber 26' L979
Mr. Efn€r G. Havcnt
Grants Offlger
National scLence Foundatlon
walhlngton' D,C. 20 550
Re!
Grant ilSER-791{33,t
Propo.al tsER-79143 3{
Dear Mr. Haveng:
of SsPtonber 14. Ple were grateThank you for your letter
ful to learn that tha Natlonal science Fouadatlon hrB nadc
a qrant of 910,315 to HoPe College for the progran' "A
lrtlcroconputer Laboratory for uae in Teachinq SLrtl8tlcr."
ThI! qrant wtll b€ ol great help to ui as we develoP ou!
program ln Mathenrtlcs.
we accapt thls gnnt
l{ncd ln your letler.
ln accorilance tith
we alk that you exCsnd our apprsclation
for liaklng thls grant
were reeponsible
Co1Ie9e.
slncerely
youra.
Gordon J. Van liylen
GwIII:c|m
bcc!
El.l.iot' tanis
-wil1ian
Analerson
tha condillons
out-
to all tho8e who
avallable
to gope
furh
l{!Mo
DATE:
Jaouary 4, 1980
T0:
Serb Dcrshen
rROU:
gheldoa Wetteck
SITBJBCT: Capltsl. cgulpDeDt cxpcEditurca
Tbl,a DeDo conatLtutea aplrroval -for you to pulcbaae tbe taroi!6l
urdcr
for uac 1! thc CoDl,utcr gcicace DcprrtDcot wbicb waa rcguclt.d
capltal
equlpD.lt.
Up to $1200 h.6 b.co a1lotlcd
for tb13 purpoi..
l{he! lt 13 prcplred !I..ae
for
f,onrard . purchaae ordcr to oy offlc.
f,laal approval and de.lSDatloa
of tb!.ccouot
alDber,
I aD arlrr[lE8
that, a! yoll rtalcd
la thc rcgu.Bt,
thts teroiall
nlll
be a13o utlllzed
lo the cooputet aclence laboratory
ead herce
corstitut€
! poltloa
of our D.tchlEg for tbe I|SF-IAEP aratrt.
If you have asy qucatiora
heaLtate to coatact DG.
cc - ?lrrot
Teale/
about thl!
cxpeoditure,
pI€are
do trot
nol
Fror.rL sctrNcgFoul._o.r
*lshingloo, D,c. 20550
REPORT
FiNAL PROJECT
lsF I,(i:lrl 93,\
'
r:.slnr'cn,l\ { a\ r,l-r tisr aff.iRE LntPll.l"1.!.
iiif,Gllln
reni i-lrolr-cr rorrrirlcATlo^iINfoR\raT"Q)i
I lMiur'on:nd AdLl*s
HoFeCollege
Ho11and,MI 49423
a. /rsdd P.nod
F,"^ t0/1/72 b
5. Cunllltive
3/37/82
Awatd Antou.t
$1 0 , 3 1 s
A l4icrocorputer Laboratory foa ljse in Teaching Statistics
/FoRPUal/ct,v
iiar ir-swvanv or cott?LElIDPRoJEqr
to provide a laboratory
T
f"rl nraio Shack TRS-80microcoDputers were puxchased
coulses' T{o printers
for
other
ard
in statistics
t"tti"f'e"t-c""tt"s
illh:t-tl1:t
n"t" fi".ftas"a to Pioviile hard coPy for sone of the output'
software were developed for use
ConDute! based eteacises ard supporting co$puter
several ways.st\.rdents
rhe nai'eriars-are ieing used in
r"
probability neet weekiy.ina laboxatoxysetting-and
""i"iiiiirriir-;;i;"i;.
i" ll.irr"^"il""i saaiistics ana
oi ptotr"tt,.i""r"aing sirulations -d 9?t1.i"lv.tit' Thesestudents
iirr""ilLilii
aPPleciation of theoretical concepts
to,'" gu]l' a greater
vaite their own proSfalls
"no
A1s6 profeisors have used the natexials'to plepale
in-oroUatifitv aird itatirt;."s'
in lowe?'lerel statistics courses' A third potential
i"t it"a"..t
;'jr#;;;;i;;;
of aft" naterials is for u[dergraduate resealch plojects'
"t"
the liberal arts student'
The conPuters have afso beerl use'l in oul course fo!
nticrocornputers
Pt9u19".1
,,Th" N;1";; ii uathenatics.,, For nany of these srudents,
are vef,y flidndly
micf,oconputers
Fortunately
conPuters:
!o
fixst hands-on exposure
foa students who fear both natheruatics and coftputers'
S t u . I e n t i n ' t h e g t a t j " s t l c s l a b o r a t o r y h a v e g i v e n p o s i . t i v e - e v a l u aploglalls
t i o n s t o t h!o
is
writo sinulation
type of educational expe:cience. The o?portunity to
concepts and tirin obtain imnediate results at the conputer
;ifir;;"i;-6;;;;;ica1'
is instructive and satisfying for then.
Fl
rlEM lche.k oPPrcPntte blockt)
Fa t t a o d Ra,rt,\ | AN.| 6 EI I F'.lf L s Es t
TO AEFURNISHII)
P R E V I O U S L Y SIil^RATE!Y TO PROGI(Ai,l
FIJRNISHEI)
b. PuUlicrtionCilations
c, Dat.ofl Sci.n ti6c Col laboJalo*
d. Inlomlriot
;lTccliiicrl
on Int.!nof,s
Descriplion ofProjecl )nd Rc(lh
IF...rpJiiiiig:to/r'nr""!DuectorN'ne/lp?d/
E11iot A. Tanls
3 P ' i n r p r l h v ! , r ' ! J t o n ? r c r . tL l t r r ! i , t s i ! r i r ' t r u
s/28/82
CONCEPTS
FORUNDERSTANDING
THE USE OF MICROCOMPUIERS
IN PROBASILITY
ANDSTATISTICS
811iot Tanis
tlope College
Holletrd, Michigan 49423
United States of Alerica
Conf,erence
the First lfltelnational
To appear in the Abstracts booklet
on Teaching Statistics, Utriversity of Sheffield, sheffield, England,
9-13 August 1982.
TIIE USEOF IIICROCOI{PI-TTERS
FORUNDERSTANDING
CONCEPTS
IIi PROBABILITY
ANDSTAT1STICS
Elli.ot Tanis
HopeCollege
HoIIand, Michisan 49423
uni.ted States of A:nerica
Conputers can be used in a variety of ways in the statistics
cutriculurn. One
way is ro help students better uldexstand basic concepts in probabitity and
stati.stj.cs. T\ro irPortarlt ingredi.ents are necessaryto accomplishthis:
(a) a good soft{ale packagethat nakes effective use of the graphics
capabilities of the conputex,
(b) exercises and exanples that have sound educational v6.1ue.
Materials have bee[ developed to acconpany a yea! long coulse in nathenatical
statistics and probability.
There.are note than 200 exercises of varying degrees of difficulty.
The supporting conputer softlrale includes subrouti.nes for:
(a) depicting a histograE aad/or an eEpirical di.stlibution function wi.th the
option of supelidlposingthe theoretical probability density function
and/o! distribution function, respectively;
(b) illustrating confidence inrervals j
(c) scatte! diaglans;
(d) giving values of i.nportant distribution
functions and thei.! inverses i
(e) siDulating randon sanples frotl several distributions.
TheseDaterials can be used in a valiety of uays. .For exanple, al1 of the
students in a class could be a5ked !o solve the exercises by wliting conpute!
plograns and, j.!t so doing, gai.n a greate! alpleciation of theoretical coocepts
ir both probability and in statistics.
0! €. professor a[d/or sode students
could solve ar exercise and prepale a deDotstlation for a statistics
class that
is taught at atry leve1,
0r a student colrld use theso natelia.ls as a Dart.of
an undelgraduateresearch projec!.
Culrently the soffiiare that has been develo?ed is written
in BASICfor the
Radio Shack TRS-80 conputelt
lhat the nalelials
l{e plarl to nake the necessary ,:bdifi.cations so
can be used wj.th an Apple colputer.
An eerlie! version of
this package is written
and can be wed in either batch or interi.n FoRTRAN
active node on oost large con?uter systens.
That lackage is distlibuted by
CoNDUIT,P.0. Box 588, Iolra City, Iowa 52240, USA.
To give sone appleciation of the types of exercises and the graphical output,
four exarnples are strmarized and one fj.gu"e is given for: each.
Exarple l.
Sinulate 200 observations of a bironial randon valiable :( fo!
{hich n = 1I and p = 0.6. use the fact that X is the sulr of 11 Bernoulli
* Ten Radi.o Shack TRS-80 conputers were purchased with support fron the
National. Science Foundation urder 6rant No. SER-7914334.
trials,
S u p e r i m p o sl eh e b i n o m i a l p
. r o b a b j . l i t y f u n c t r o n o n l h e r e . L a t i v ef r e q u e n c y
histogran of the obseivations of X.
Exanple l.
Illustrate
See Figure I for a t)?ica1 solution.
empirically that the sun of lNo ,,randonnunbers,,,
selected at randomfron the interval
(0,1), has a triangulat distribution.
Superimposethe probability density function on the relative flequency histogran of 200 obsetvations of surs of paits of randon nunbers. See Figure 2.
Exanple 3. Sinu]ale 50 randon sanples of size 10 flon a nornal distlibution
having mean! = 40 and valiance o'= 12. For each sanpleJ calculate the endpoints for a 90%coDfidenceinlerval for u, assuning that u and o' are unkno,rn,
using i + 1.833s//id'. The confidence intervals are depicted in Figure 3. A
= 40,
horizonral line is draNn at u = Ptr'!
Sinulate a randon sanple of size n = 50 fron a bivariate nomaL
distribulion for whichu., = s0. o: = 36. 8.. = 70, o: = 64, ando = 0.75.
Exar0pl.e
4.
Figure 4 shovs a scatter plot for such a sinulation.
tucrlfil
HIsI(frdr PR0mIILITY
iE-n u! Fnrrt.af,y
9.at
REAIlttF[€[OrtlFl(m{ | Pl0slLln F6llY tufTlttl
l.a9
9.,45
8.i5
0.i?
8.10
0,48
0.6
0.e{
s,00
9,8N
8 r { 6 | 4 D r s r r r l d t o . ,r ' l l ,
sH or tu 'wocr tmi3'
.'0.6
FIGURE1
cftfltat€ finsl{r.s
!2.:0
S€AIIEIIOI
s.m
4i,!€
€.5€
.1,7,:€
t6.tt
p.50
68,4{
a:.s
5{.00
n'lc
R.m?f I1{S s l lEi/ltscg|rAl
, :l 't
lfflt )i: {9.6-! ,t{
f;m
$ 3{.€l atrm. lm c0fF! 0.i69
ljm
$ 56,s
|tifl I: :0,ts
FIGURE4
PARTIII
1.c.
. TECHNICAL
]NFOR}dTTION
Data on Scientific
Collaborators
Heibert L. Dershem
Professor of llathenatics
Hope College
Ho11and, MI 49423
1.e.
and Conputer Science
Technical Description of Project and Results
The puf,poseof this project was to establish a nicroconputer laboiatory to
enhance the learining of statistios,
Wepurchased the proposed equipnent and
established a conputer laboratorl i.n a roornin the college library.
The
college library is adjacent to the nathedatics building. By having the
laboratory in the library, we believed that it would be readily available to
all of our students. This concept net rrith tnixed success. Students did
appreciate the availability of the conputers. Ho{ever becausewe did not
continuously supefiise the conputels, we did have note equipnent failures than
we would have 1iked.
This cordng year pernanent space !/i11 becone available in the nathenatics
buildj.ng. Hope College has coflmitted sone of this space fo! the nicroconputer
laboratoxy and funds to supervise this laboratoay.
Becauseof the availabi.lj.ty of a microcoilputer laboratory, we have been
developing educatiorEl naterials that nake use of this equiprent, Thus fa!
good progress has been nade in the developnent of riaterials for our statistics
coutse.