hw6 - 
 Homework
Assignment
6
 Psychology
60
...

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Unformatted text preview: 
 Homework
Assignment
6
 Psychology
60
 Spring
2010
 
 
 
 General
Instructions:
 ‐ Make
sure
your
homework
has
written
on
it:
 o YOUR
NAME
 o YOUR
STUDENT
ID
 o YOUR
TA’S
NAME
(you
can
find
this
on
the
syllabus)
 
 ‐ Please
be
sure
your
homework
answers
are
LEGIBLE.
 
 ‐ For
homework
problems
requiring
calculation,
you
must
show
all
of
your
work,
 including
intermediate
steps,
in
order
to
receive
credit.


 ‐ Please
circle
final
answers
to
problems
that
require
computation;
doing
this
will
make
sure
 we
can
find
your
final
answer.

 ‐ For
questions
requiring
a
short
written
answer,
be
as
concise
as
possible
while
still
 explaining
your
answer.

 
 ‐ If
you
have
questions
about
concepts,
feel
free
to
post
questions
on
the
class
discussion
 board.
You
may
also
email
your
TAs,
but
do
so
only
after
you
have
looked
through
the
book
 for
an
answer
to
your
question.

 ‐ Homework
is
due
at
the
start
of
class
on
Tuesday
(by
11:15).
No
late
homework
will
be
 accepted.
 
 
 1) Find
the
tcritical
values
for
a
two‐tailed
hypothesis
test
with
 α = 0.05 
for
the
follow
values
of
 df:
 a. df
=
2
 b. df
=
8
 c. df
=
20
 d. df
=
40
 
 2) The
following
scores
were
obtained
from
a
population
with
unknown
parameters.

 Scores:
6,


12,


0,


3,


4
 a. Compute
the
sample
mean
 b. Compute
the
estimate
of
the
population
variance
 c. Compute
the
estimate
of
the
standard
error,
 s X 
 
 3) To
evaluate
the
effect
of
a
treatment,
a
sample
of
n
=
9
is
obtained
from
a
population
with
a
 mean
of
μ
=
40,
and
the
treatment
is
administered
to
the
individuals
in
the
sample.
After
 treatment,
the
sample
mean
is
found
to
be
 X = 33 
 a. If
the
sample
has
a
variance
of
s2=81,
are
the
data
sufficient
to
conclude
that
the
 treatment
has
a
statistically
significant
effect
using
a
two‐tailed
test
with
 α = 0.05 ?
 4) 5) 6) 7) b. If
the
sample
has
a
variance
of
s2=225,
are
the
data
sufficient
to
conclude
that
the
 treatment
has
a
statistically
significant
effect
using
a
two‐tailed
test
with
 α = 0.05 ?
 c. Comparing
your
answers
in
A
and
B,
how
does
the
variance
you
calculate
for
your
 sample
affect
the
outcome
of
a
hypothesis
test?
 
 Some
research
examining
the
effects
of
preschool
childcare
has
found
that
children
who
 spend
time
in
day
care,
especially
high‐quality
day
care,
perform
better
on
math
and
 language
tests
than
children
who
stay
home
with
their
mothers.
A
typical
result
in
this
area
 might
show
that
a
sample
of
n=25
children
who
attended
day
care
before
starting
school
had
 an
average
score
of
 X = 87 with
SS
=
1536
on
a
standardized
math
test
for
which
the
 population
mean
is
μ
=
81.

 a. Is
this
sample
sufficient
to
conclude
that
the
children
with
a
history
of
preschool
 daycare
are
statistically
significantly
different
from
the
general
population?
Use
a
two
 tailed
with
 α = 0.01 .

 b. Compute
the
estimate
of
Cohen’s
d
to
measure
the
size
of
the
preschool
effect.
 c. Write
a
sentence
showing
how
the
outcome
of
the
hypothesis
test
and
the
measure
of
 effect
size
would
appear
in
a
researchreport.

 
 In
a
two‐sample
study,
one
sample
has
SS
=
48
and
a
second
sample
has
SS=32.

 a. Assuming
n=5
for
both
samples,
find
each
of
the
sample
variances
and
compute
the
 pooled
variance
(because
the
samples
are
the
same
size,
you
should
find
that
the
 pooled
variance
is
exactly
halfway
between).
 b. Now
assume
that
n=5
for
the
first
sample
and
n=9
for
the
second
sample.
Again
 calculate
the
two
sample
variances
and
the
pooled
variance
(you
should
find
that
the
 pooled
variance
is
closer
to
the
variance
of
the
second
sample).

 
 Two
separate
samples
receive
two
different
treatments.
The
first
sample
has
n=9
with
 SS=710,
and
the
second
sample
has
n=6
with
SS
=
460.

 a. Compute
the
pooled
variance
for
the
samples
 b. Calculate
the
estimate
standard
error
for
the
sample
mean
difference
 c. If
the
sample
mean
difference
is
10
points,
is
this
enough
evidence
to
reject
the
null
 hypothesis
using
a
two‐tailed
test
with
 α = 0.05 
 d. If
the
sample
mean
difference
is
13
points,
is
this
enough
evidence
to
reject
the
null
 hypothesis
using
a
two‐tailed
test
with
 α = 0.05 
 
 An
independent‐measures
research
study
was
used
to
compare
two
treatment
conditions
 with
n=12
participants
in
each
treatment.
The
first
treatment
has
a
mean
of
 X1 = 55 and
 2 variance
 s12 = 8 ;
the
second
treatment
has
a
mean
of
 X2 = 52 and
variance
 s2 = 4 .
Do
these
 data
indicate
a
statistically
significant
difference
between
the
two
treatments?
Use
a
two‐ tailed
test
with
 α = 0.05 .

 
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