The document discusses various statistical tests, including t-tests for single samples, paired samples, and independent samples, as well as ANOVA for comparing group means. It outlines specific examples and questions related to conducting these tests, including calculating degrees of freedom and understanding hypotheses. The document serves as an assignment or study guide for understanding the application of these statistical methods in research.

1. Assignment 4
Chapter 10
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

2. (
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

3. 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

4. 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

5. 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

6. 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.
a.
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

7. 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

8. 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

9. .
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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. g
nifi
can
t
?
Ex
pl
a
in
.
b.
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

17. 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.

18. 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

19. r
d
s the
compan
y
. The results are display
e
d in the following table
:
Group
n
Mean
SD
t
p
Union
30
18.30
9.85
1.92
.03

20. Managers
28
23.07
9.07
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.

21. 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

22. )
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:
Scores
Mean
SD
t
p

23. Pretest
18.30
9.85
7.13
.0001
Posttest
22.10
1.26
c.
10.18
.
A
pl
a
nt mana
g
er randoml
y
di
v
id
e
s her emplo
y
e
e
s into t

24. 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
,

25. 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

26. 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

27. '
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

28. 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

29. 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

30. 2
.008
B
30
3
.
00
1.
2
6
t
crit
(
.
0
5
,
d
f
)
=
2.0
;
t crit
(
.
02
,
d
f
)

31. =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

32. 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
.

33. 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

34. 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

35. 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

36. 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

37. 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= 635.13
SD= 71.53
t value= 3.75
p=.0001

38. d.
a.
Which
t
test is used and
w
h
y?
b.
What ar
e
the degree
s
of freedom
(df)?
c.
Wh
a
t ar
e
Joe
'
s con
c
lusions? Explain
Chapter 11
11.1.
While a

39. 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

40. .
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

41. 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 the
sum 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.

42. 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.

43. 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.

44. 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

45. i
t
(
.
O1,2
,
20)
=
5.85
a.
Compute the
obtained F
ratio.
b.
Determine whether the results are statistically significan
t
.
c.
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

46. ,
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

47. 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

48. 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

49. 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

50. 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

51. 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

52. 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

53. 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

54. 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

55. 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.