ff
Example
1:
Emily
Is
curious
about
the
average
lengih,of
the
female
blue
whales
that
rnlgf't'::
n:
the
California
coasl.
She
takes
a
Wo
emale
blue
whales
from
this
popula!
%
g
Their
average
recorded
length
is
¥
=
75
m
and
their
slandard
deviation
is
s,
=
11
m.
The
X
]
distribution
of
lengths
in
the
sample
is
roughly
symmetric
with
no
obvious
oulfiers,
Show
that
the
3
con
ditions
for
inference,
Random
Sample,
Independent
Trials
and
Normal
Approximation
are
salisfied.
d
l
()
fandonn
samp
C'l
e
.
%
=
1
'@
dgndtiht
T
talg
;o
=
poo
6005
¢
o.(0
A
i
l
@
VfilHMl
AFPrDy'LY\ahOV\
YMQV"
AlWWIhUV\
\(
S\{W\.hnvr{'u(
(///
sutlions

Students'
t
distribution
&is
vakhowly
3
+
ditkib
v
i
The
Student's
tdistributions
(or
simply
tdistributions)
are
a
family
of
distributions
thak

represent
the
sampling
distributions
of
the
(test
statistics
for
the
sample
mean,
1,
=
i':!
.
n
y
when
conditions
are
satisfied.
These
(distributions
have
a
similar
shape
(o
the
normal
CUf"e
'
but
wider
spreads
and thicker
tails,
so
more
of the
probability
is
contained
in
(he
tails.
This
leads
to
higher
critical
values
than
those
of
the
normal
curve
thus
creating
wider
confidence
intervals
and
higher
pvalues
than
normal
distributions.
The
exact
shape
of
a
tdistribution
is
detcrmined
by
its
degrees
of
freedom.
The mare
degrees
of
frecdom,
the
more
similar
the
(distribution
is
(o
the
normal
distribution;
in
fact,
you
can
interpret
the
normal
distribution
as
a
(distribution
with
e
degrees
of
freedom!
Sample
means
from
samples
of
size
n
will
create
a
tdistribution
with
u
—

degrees
of
frecdom.
theqrees
ot
fed
Distribution
oo
"
=

am
o
i
Ghat

l
0
fest
statistic