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STA2020F 2009Class Test 1
Date: 27thMarch 2009 Time: 1 hour 30 minutesTotal marks: 70
Instructions: Answer all the uestions in !our "lue answer "ook#
$ouranswer shoul% "e T or F &or each uestion in section A an% a
writtenanswer &or section '# There is no (enalt! &or
incorrect answers in sectionA# A &ormula sheet an% the rele)ant
statistical ta"les are (ro)i%e% at theen% o& this test
(a(er#
SECTION A: Total marks
6
State whether each of the following statements is true (T) or
false (F). Eachquestion carries 1 mark.
1) If we reject a null hypothesis at the 5 le!el of significance
then we mayor may not reject it at the " le!el of significance.
#) If the significance le!el of a test is state$ as %& then
a p'!alue of .#5woul$ lea$ us to reject the alternate hypothesis
for the test.
%) n article in an anthropology journal reports a p'!alue of .*%
for testing
+, 0 = against +1, - . If the authors ha$ instea$ reporte$ a
5
confi$ence inter!al for & then the inter!al woul$ not ha!e
containe$ /ero.*) 5 confi$ence inter!al for is gi!en 0y (%& 5).
If we were testing +,
2 %.#& then we woul$ not reject the null hypothesis.5) If
you were testing whether the mean ST1S mar3 for the stu$ents in
the #5 class was the same for male an$ female stu$ents&
theappropriate null an$ alternate hypotheses woul$ 0e, +, 4male-
4femalean$+1, 4male2 4female.
") ne of the a$!antages of using 67 instea$ of multiple t'tests
to testfor a $ifference 0etween population means& is that the
o!erall pro0a0ility ofma3ing a type I error is re$uce$.
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SECTION B: [Total marks 64]
*uestion 1(a) 8hat are the assumptions of 679 :%;
(0) 8hat is meant 0y the concept of interaction in a two factor
factorial$esign9 :#;
(c) 8hat are the $istinguishing features of the one factor 67
completely
ran$omise$ $esign& ran$omise$ 0loc3 $esign& an$ two
factor factorial
$esign9 :%;
($) ;
Sources o& +ariation %& Sum o&
Suares
Mean
Suare
F
Factor # >Factor ? ## 11.
? interaction > 1Error %
Total
(e) 8ith reference the 67 summary ta0le a0o!e&
I. t the .5 le!el of significance& what is the upper 'tail
critical !alue
from the F $istri0ution for the (1) interaction effect9& (#)
factor
effect9& an$ (%) factor ?9 :%;
II. 8hat is your statistical $ecision with respect to the
interaction effect9
:1;
,Total marks 20-
*uestion 2n e=periment was carrie$ out to compare fi!e $ifferent
0ran$s of automo0ile oilfilters with respect to their a0ility to
capture foreign material. sample of ninefilters of each 0ran$ was
use$& resulting in the following sample mean amounts,
1 2 3 414.5, 13.8, 13.3, 14.3,x x x x= = = = an$ 5 13.1.x = The
67 ta0le 0elow
summarises the first part of the analysis.
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Sources o& +ariation %& Sum o&Suares
MeanSuare
F
Treatment (0ran$s) * 1%.%# %.%% %@.>*
Error *
%.5% .>>
Total **
1".>5
(a) State the appropriate null an$ alternati!e hypotheses.
:#;
(0) Test at the .5 le!el of significance for any $ifferences in
the true
a!erage a0ility to capture foreign material $ue to the $ifferent
filter 0ran$s.
:#;
(c) 8hat is a A'7alue of a hypothesis test9 :1;
($) 8hen $oes a A'7alue pro!i$e e!i$ence against the null
hypothesis9 :#;
(e) Estimate the A'7alue of the e=periment a0o!e an$ comment on
the result.
:*;
(f) Bsing Tu3eyCs metho$& at the .5 le!el of
significance& perform a multiple
comparisions analysis to i$entify significant $ifferences among
0ran$s.
8hat is your conclusion9 :5D1;
(g) 8hy woul$ Tu3eyCs proce$ure 0e preferre$ to FisherCs S
metho$9 :%;
,Total marks 20-
*uestion 3ata were collecte$ a0out the performance of chil$ren
in 1* schools. Thechil$ren too3 an aptitu$e test 0efore going to
the schools& an$ then they sat anational test in mathematics
fi!e years later. The researchers e=pecte$ there to0e a
relationship 0etween a chil$Gs scores in these two tests. The mean
scores
were presente$ for each of the schools& an$ are gi!en in the
ta0le 0elow.
School Mean score on aptitude test Mean score on
mathematicstest
1 @." **."
# "1.5 51.
% "@.% 5.#
* @.% >5.@
5 "5.# 5%."
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" "*.% 5".1
@ "@.5 *#.>
> ".# 5#.#
"". %.1
1 >.5 @*.@
11 5#.* *1."
1# @.* *.*
1% "*.# 5%.@
1* ">.* %."
portion of output from the fitting of a simple linear regression
mo$el is gi!en0elow& with some entries $elete$,
Hoefficient
SE T'Stat
A'7alue
Honsta
nt
'#".1* #.1* '. .%>@
ptitu$e
1.1@%# .*%#@
nalysis of 7ariance
Sources o& +ariation %& Sum o&
Suares
Mean
Suare
F P-
+alueegression 1 #1.* #1.* @.%
5.1
Error 1#
15*.# 1#5.%
Total 1%
#*#5."
(a) 8rite $own the equation of the fitte$ mo$el. Try to gi!e
an
interpretation of the two parameter estimates in the fitte$
mo$el. :%;
(0) Halculate the coefficient of $etermination an$ interpret
this figure. :#;
(c) +ence fin$ AearsonCs correlation coefficient 0etween the
!aria0les.
Test this correlation coefficient for significance. :5;
($) Houl$ the true regression line pass through the origin9
E=plain your
answer 0y referring to the output a0o!e. :#;
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(e) Houl$ the true slope of the regression line 0e /ero9 Harry
out the
appropriate test& gi!ing a p'!alue (as far as the ta0les
will allow) in your
conclusion. :*;
(f) Fin$ the resi$ual associate$ with the first school in the
sample. :#;
(g)
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&o'u(ns SS*+ ) 1 MS*+ MS*+/MSE F, )-1. n-)$nter)t!on SS*B+
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MSETOTAL SS(Total) n !
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-ult"pl$ r$,r$ss"on:
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1o$"."$nt o mult"pl$ $t$rm"nat"on: [ ]
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1o$"."$nt o part"al $t$rm"nat"on:R F
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+$,r$ss"on ANOVA tal$:
df SS MS F Sig F
#egress!on k SS# MS# 6 SS#/k MS#/MSE 7*Fk, n-k-1 F+
#es!u)' n-k-1 SSE MSE 6 SSE/*n-k-1+TOTAL n! SST
Tt$st stat"st".: 45 6 1
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=
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