10.1. In a t test for a single sample, the samples mean.docx

10.1. In a
t
test for a single sample
,
the sample
'
s mean is
c
o
m
par
ed to the
population
.
10.2. When we use a paired-samples
t
test to compare the pret
es
t and
p
ostt
est
scores for a group of 45 people, the degrees of freedom
(
df
)
ar
e _____.
10.3. If we conduct a
t
test for independent samples
,
and
n1

=
32 and
n2
=
35,
the degrees of freedom
(df)
are
_____.
10.4
.
A researcher wants to study the effect of college education on p
eo
p
le's
earning by comparing the annual salaries of a randomly
-
selecte
d g
ro
up
of 100 college graduates to the annual salaries of 100 randoml
y-selected
group of people whose highest level of education is high
schoo
l.
To
compare the mean annual salaries of the two groups
,
th
e resea
r
cher
should use a
t
test for

______.
10.5. A training coordinator wants to determine the
effectiveness
of a program
that makes extensive use of educational technology when t
raining new
employees. She compares the scores of her new emplo
yees who
completed the training on a nationally-normed test to th
e
me
a
n
s
c
ore of
all
those in the country who took the same test.
The a
p
pro
p
riate
statistical test the training coordinator should use for h
er analysis
i
s the
t
test for ______.
10
.
6. As part of the process to develop two parallel forms o
f a q
u
es

t
io
nn
aire
,
the persons creating the questionnaire may admin
i
st
e
r b
o
th
f
or
ms to a
group of students, and then use a
t
test for ______ s
a
mpl
es
t
o com
p
are
the mean scores on the two forms
.
Circle the
correct
answer:
10.7. A difference
o
f 4 points between two
homogeneous group
s
is lik

e
ly to
be
more/less
statistically significant than the
s
ame
d
i
ffe
r
e
n
ce (of 4
points) between two
heterogeneous
groups
,
when all fou
r g
r
o
up
s are
taking completing the same survey and have appro
x
im
a
tel
y t
h
e same
number of subjects.
10.8. A difference of 3 points on a 100-item test taken b
y t

w
o g
rou
ps is likely to be
more/less
statistically significant than a difference of 3 po
i
nt
s on a 30-item test taken by the sa
m
e
t
w
o g
r
oups.
10.9 When
a
t
test for paired samples is u
s
ed to
c
ompare th
e
p
re
t
est an
d
the posttest
means
,
the number of pretest scores i
s
the

same as/different than
the number of
po
s
t-t
e
st scor
e
s.
10.10. W
hen
w
e
w
ant to compar
e w
h
e
th
e
r female
s
' scor
es
on th
e
G
MAT are
di
fferent f
rom males' scores
,
we should use a
t
test for

paired samples/independen
t
samples
.
10
.11 In studi
e
s
w
h
e
re the alte
r
nati
ve (
r
es
ear
c
h
)
h
y
poth
es
i
s
i
s
directiona
l
,
t
h
e critical va

lu
es
for
a
one tailed test/two-tailed test
should b
e us
ed t
o
d
e
t
erm
i
ne the
l
e
vel o
f
signi
fi
cance (i
.
e.
,
the
p
va
lue).
10.12 W
h
e
n
t
h
e

alt
e
rnati
ve
h
y
poth
e
si
s
is: H
A
: u1=u2
,
the c
ri
ti
ca
l
v
alu
es for
one
tailed test/
two-tailed
test
should b
e
u
se
d to det
er
mine the l
eve
l
of statist

i
cal s
ignificance
.
10.1
3
.
In
a
s
tudy
c
onduct
e
d t
o
compa
re
th
e
test
s
cores of e
x
perim
ental and control g
roup
s
,
a 50-it
e
m t
est
i

s a
dmini
s
t
e
red to both
g
roups at th
e e
n
d of t
h
e study. The me
an
of
th
e ex
p
er
im
e
n
ta
l group on th
e
te
s
t i
s
1 point h
ig
h
er than the mean of
th
e c
ontrol g

r
oup
.
T
he
re
search
ers
conduct a
t
tes
t for ind
e
p
endent samples to c
ompar
e
th
e
two means
.
The
o
b
t
ain
ed t
v
a
lue is 1.89
,
and th
e p-value is
.
05. C
an

w
e con
c
lud
e
that th
e ex
periment
a
l tre
a
tment
w
a
s
c
l
ea
rl
y effective
because t
h
e
t
v
alue
is
s
ta
t
i
stic
all
y s
i
g

nifi
can
t
?
Ex
pl
a
in
.
10.14. Identify each of the following as a
null
h
y
pothesis
,
a
dir
ect
io
na
l
h
y
pothe
s
i
s
,
or a
non-directional
hypothesis.
a. mean 1does not equal mean 2 is a ______ hypothesis
b. mean 1 does equal mean 2 is a __________hypothesis
c. mean 1 is greater than mean 2 is a ________hypotheses
d. mean 1 minus mean 2 equals zero is a _______hypothesis

10.15. A compan
y
ps
y
chologist wants to compare the scores of a g
r
oup
of 35
employees on two different IQ tests: one is a group IQ test and
on
e
i
s a
n individually-administered IQ test. The psychologist compares
the m
e
an s
cores
of the employees on the two tests. Which
t
test should the psychologist u
s
e
to
determine whether there is a significant difference between the t
w
o s
e
t
s of IQ
scores? Explain.
10.16. The CEO of ABC Company wishes to determine whether
there ar
e diffe
r

enc
e
s
between union members and managers in their attitude to
w
ard the
c
omp
an
y
.
The CEO asks 30 randomly selected union member
s
and 28 m
a
n
age
r
s
t
o
complete a 40-item questionnaire designed to measure attitud
es towa
rd
th
e
company
.
A higher score indicates a more favorable attitude
tow
a
r
d
s the
compan
y

. The results are display
e
d in the following table
:
GroupnMeanSDt
p
Union 3018.309.85
1.92.03
Managers2823.079.07
a. Which
t
test should the CEO use to compare
th
e
re
s
pons
es of the
union members and the managers? Explain
.
b. What are the degrees of freedom?
c. What are the conclusions of the CEO based on the result
s i
n th
e t

ab
le
?
Explain.
10
.
17. Based on the results of the study described in the previous
question
,
the
CEO
and the HR manager decide to implement several program
s
to
g
et
t
h
e
uni
on
more actively involved in making decisions at ABC.
A
fter
i
mplement
in
g
t
h
e
programs for a year
,

the CEO asks the same group of union members
(
n=3
0
)
t
o
about their attitudes towards the company again
,
using the same qu
es
ti
o
nna
ire
as the one used the
y
ear before. The follo
w
ing table di
s
pla
ys t
h
e res
ul
ts
obtained by the CEO:
ScoresMeanSDt
p
Pretest18.309.85
7.13.0001
Posttest22.101.26

10.18
.
A
pl
a
nt mana
g
er randoml
y
di
v
id
e
s her emplo
y
e
e
s into t
wo g
ro
ups
.
One group (
Group A) in
c
ludes 32 employees
a
nd th
e
second one
(

Gr
o
up B
) i
n
c
lu
des 30 e
mplo
ye
e
s. A
ft
e
r di
v
iding th
e e
mplo
ye
e
s
,
th
e
mana
ge
r
wa
n
ts
t
o co
n
firm that t
he two group

s
a
r
e ind
e
ed similar in p
e
rformanc
e
. He h
y
pothesi
ze
s
tha
t
t
h
ere is
no statisti
c
all
y s
i
g
ni
f
i
c
ant di
f
fer
e
n
ce
b

e
t
we
en th
e tw
o group
s. To c
o
mpare the
t
w
o groups
,
the plant manager use rating
s
gi
v
en b
y
the
e
mplo
yees
'
fr
o
n
t
-li
n
e s
up
e
r
v
isors at th

e e
nd of th
e
pre
v
iou
s y
ear. The ratin
g
scal
e r
an
ges fr
om
5
(exc
e
ll
e
nt
e
mplo
y
ee
)
to 1
(
on the brink of termination
)
. U
s
ing the
se
r
a
tin

gs
,
the
mana
ge
r conducts a
t
t
e
st to determine
w
h
e
th
e
r th
e
t
w
o
g
roups
a
r
e s
imilar.
Th
e
r
e
sul
ts a
r
e
a
s

follo
ws
:
Group
n
M
e
an
SD
t
A
32
3
.66
1.
3
1
2
.008
B
30
3
.
00
1.
2
6
t

crit
(
.
0
5
,
d
f
)
=
2.0
;
t crit
(
.
02
,
d
f
)
=2
.
3
90
;
t
cri
t
(
.
01
,
df
)
=

2.660
a.W
hich
t
t
es
t
w
as us
e
d and
w
h
y?
b.W
hat
we
r
e
th
e
degr
ee
s of fre
e
dom?
c.
What ar
e
th
e
mana
ge
r
'
s conclusi

o
n
s? Ex
plain.
10
.
19
.
Joe
,
a new manager su
s
pects th
a
t the 23 n
e
w emplo
yees assig
n
ed to h
i
s
d
e
p
a
rtment h
ave

lo
w
e
r
le
v
el
s
of
s
ocial
s
kill
s
than the ne
w e
mpl
oyees hired into
the all the other departments in the rest of the company
.
The
c
om
pany gives all
pro
s
pect
ive
emplo
ye
e
s
a social
s
kill
s a

ss
e
ssment b
e
fore b
e
in
g
h
ired
.
The m
e
an s
cor
e
obtained by Joe
'
s new
e
mplo
y
ee
s
i
s
635.13
a
nd th
e
m
ea
n
score of
al
l

678
n
ew e
mplo
ye
e
s
recentl
y
hir
e
d b
y
th
e c
ompan
y
on the
s
am
e social skills as
se
s
sment i
s
430 (fl
=
430
)
.
A
t
te
s
t i
s

used to compar
e t
h
e soc
i
al skills asses
sm
e
nt
sc
or
es
of Joe
'
s ne
w
emplo
ye
es to all th
e
n
ew em
p
l
o
yees in the c
ompan
y.
Th
e
r
es
ults o
f
the
t

t
e
st
ar
e:
Mean score= 635.13SD= 71.53t value= 3.75 p=.0001
d.
Which
t
test is used and
w
h
y?
What ar
e
the degree
s
of freedom
(df)?
Wh
a
t ar
e
Joe
'
s con
c
lusions? Explain
11.1. While a
t

test is used to compare
two
means
,
the one
-
way ANOV
A
c
a
n be used to simultaneously compare ____ groups.
11.2. An ANOV A is considered to be an extension of the
t
test
f
o
r
independent samples because both investigate differences bet
w
een ______.
11.3. By conducting a one-way ANOVA test to compare
multiple (more than 2) group means
simultaneously
instead of conducting a series of
t
tes
ts
to compare these means
,
the potential level of ____ is reduced
.
11.4. In order to appl
y
the ANOV A test
,

the data should be measured on a
(n)
_____
or
______
scale .
•
11.5. The one-way ANOV A is used when there is/are
____indepe
n
d
ent
variable(s).
11
.
6
.
With 3 groups
,
the null h
y
pothesis
(H
o
) in
ANOV
A
is
: __________.
11.7. The
total
(or
grand)
mean in ANOV A can be thought of as the mean o
f ____.
11.8. The SSw

(within
-
group
s
sum of squares) and the SSg
(betwee
n
-
groups
sum of squares) are equal to thesum of squares.
11.9. To find the MS
g
,
we divide the SSg by _________.
11.10. To compute the
F
ratio, we divide the ______ mean squar
e
b
y t
he
_________
mean square.
11.11
.
Factorial ANOVA is commonly used when there are at lea
s
t ______ independent variables.
Circle the
correct
answer:
11
.
12. The following is an example of a(n)

null/alternative
h
y
pothesi
s i
n
AN
O
VA:
Mean one does not equal mean 2 and/or mean one does not
equal mean 2 and/or mean 2 does not equal mean 3
11.13
.
Post hoc comparisons should be conducted in cases
w
here the
F
ra
t
io
is/is not
statistically significant.
11
.
14
.
The
F
ratio is likely to be statistically significant when the differenc
es
be
tw
e
en
the group means are
small/large

.
.
11.15
.
The
F
ratio is more likely to be statistically significant when it is used
t
o
anal
y
ze scores from groups that are
homogenous/heterogeneous
in regar
d t
o the characteristic or behavior being measured.
11
.
16. An ANOVA procedure is used to analyze data from a study
comparin
g
s
cores of three
groups
.
Following are the obtained mean squares and
t
he appropr
i
at
e
critical
values
for the

F
ratio at
p=.05
and
p=.01
F
crit
(.
05
,
2
,2
0)
= 3.49 and
F
c
r
i
t
(
.
O1,2
,
20)
= 5.85
Compute the
obtained F
ratio.
Determine whether the results are statistically significan
t
.
Report your conclusions.

1
1
.17. Three different age groups of consumers (ages 18-25
,
26-35
,
36
-45) in two
different regions of the country (Midwest
,
South) were sur
v
e
y
ed
a
b
out the
i
r
likelihood of buying a new product. Following are the means a
n
d
st
and
ard
deviations obtained by the three age groups in each of the two
regions
:
Means
Standard Deviations

Ages
Ages
Ages
Ages
Ages
Age
s
Region
18-25
26-35
36-45
18-25
26-35
3
6
-45
Midwest
50.2
52.8
53.3
2.
5
3.1
2.
7
South
41.0
48.5
55.9
2.
7
3.
2
2.
8

Two
separate
one-way ANOVA procedures are conducted
to
test
whet
h
er the
differences between the three means of the three age groups
i
n
e
ach
of
th
e two
regions are statistically significant.
Estimate
which
F
ratio w
o
uld be
l
arge
r: The
one resulting from analyzing the survey results obtained
fr
o
m
th
e t
hre

e ag
e groups in the Midwest or the one from analyzing the surv
ey re
s
u
l
t
s ob
t
ain
ed by
the three age groups in the South explain your answer.
11.18. Three statistics classes at University A took the same
t
est a
s d
i
d 3 other
statistics classes at College B. Following are the means and s
t
andard de
viation
s of the 3 classes in each of the two schools
:
Means
Standard Dev
i
ations
SCHOOL
Stats

Stat
s
Stats
Stats
S
tats
S
t
a
t
s
Class I
Class 2
Class 3
Class I
Class 2
Cla
ss 3
University A
71.4
78
.
8
90.2
3.2
4.3
4.8
Colle
ge B
72.1
78.6
89.3
9.3
6.6
8

.
7
Two
separate
one-way ANOVA procedures are used to tes
t wh
eth
er the
differences between the means in each of the two schools
a
r
e s
ta
tistically
significant.
Estimate
which
F
ratio would be larger
:
the one
resu
lt
i
n
g from
analyzing the test scores obtained by the three groups at Univ
er
s
ity A or the one
resulting from analyzing the test scores of the three groups
at Coll
e
ge B
.
Explain your answer.

11.19
.
Each of the two figures below (Figure A and Figure
B
)
depicts
a set of 3
distributions. Two
separate
one-way AN OVA analyses ar
e
per
f
o
r
m
e
d
to tes
t whether there are statistically significant differences between
th
e
three me
ans in
each set and two
F
ratios are computed. Estimate which of the
tw
o
F
ra
t
ios is
likely to be higher and explain your answer.

11.20. In a study comparing means of 4 groups, the
F
ratio was significant at the
p<.0
5
level
.
The 4 means are Mean 1=13
.
12; Mean 2=9.31; Mean 3=13.65
;
and Me
an
4
=
11.34. Tukey's post hoc comparison is used to test which means
statisticall
y
differ from each other. The
obtained
HSD value at the
p=.05
level is 3
.
74
.
Which means are statistically significantly different from each
other? Expla
i
n
.
11.21. A pilot-test marketing research study comparing two new
models of
w

idgets was conducted in two companies (Company A and
Company B)
.
In each of
t
he two companies, one manufacturing plant used one new
widget and the other plant used the other new widget
.
At the end of the year, the employees using the new widgets in
their jobs completed a questionnaire assessing their satisfaction
with the widgets. Following is a table listing the mean scores of
the two plants questionnaire scores for each of the two
companies (those that used new widge
t
1 and those that used new widget 2). Study the data in the table.
(Note
:
Do no
t
attempt to compute the F ratios or the exact level of significanc
e i
n order
to
answer the questions below
.
)
Means of
Means of
Company
Employees Using
Employees Using
Widget 1
Widget 2
Company A

55
53
Company B
50
48
a.Are there differences in questionnaire scores as a result of the
using the two widgets? Explain.
b.Are there differences in questionnaire scores between the two
companies?
Explain.

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