# HP 50g User Manual Page 616

Graphing calculator.

The following table shows how to select the numerator and denominator for F
depending on the alternative hypothesis chosen:
____________________________________________________________________
Alternative
hypothesis
____________________________________________________________________
2
2
H
:
<
(one-sided)
1
2
2
2
H
:
>
(one-sided)
1
2
2
2
H
:
(two-sided)
1
2
___________________________________________________________________
(*) n
is the value of n corresponding to the s
M
corresponding to s
____________________________________________________________________
The P-value is calculated, in all cases, as: P-value = P(F>F
The test criteria are:
Reject H
if P-value <
o
Do not reject H
Example1 -- Consider two samples drawn from normal populations such that n
= 21, n
= 31, s
2
2
2
=
, at a significance level
2
2
2
H
:
. For a two-sided hypothesis, we need to identify s
1
2
follows:
s
M
s
m
Also,
.
m
if P-value > .
o
2
= 0.36, and s
1
2
2
2
=max(s
,s
) = max(0.36,0.25) = 0.36 = s
1
2
2
2
2
=min(s
,s
) = min (0.36,0.25) = 0.25 = s
1
2
n
n
= n
N
= n
D
Test
statistic
2
2
F
= s
/s
o
2
1
2
2
F
= s
/s
o
1
2
2
2
F
= s
/s
o
M
m
2
2
s
=max(s
,s
M
1
2
, and n
M
2
= 0.25. We test the null hypothesis, H
2
= 0.05, against the alternative hypothesis,
= n
= 21,
M
1
= n
= 31,
m
2
- 1= 21-1=20,
M
-1 = 31-1 =30.
m
Degrees
of freedom
= n
N
2
= n
N
1
= n
N
M
2
2
2
), s
=min(s
,s
m
1
is the value of n
m
) = UTPF(
o
2
1
2
2
o
-1,
= n
-1
D
1
-1,
= n
-1
D
2
-1,
= n
-1
D
m
2
)
2
,
,F
)
N
D
o
1
:
o
and s
, as
M
m
Page 18-49