HP 49g+ - Manual (Page 615)

Page 18-48
Inferences concerning two variances
The null hypothesis to be tested is , H
o
: σ
1
2 = σ
2
2 , at a level of confidence (1-
α)100%, or significance level α, using two samples of sizes, n
1
and n
2
, and
variances s
1
2 and s
2
2 . The test statistic to be used is an F test statistic defined
as
2
2
D
N
o s
s
F =
where s
N
2 and s
D
2 represent the numerator and denominator of the F statistic,
respectively. Selection of the numerator and denominator depends on the
alternative hypothesis being tested, as shown below. The corresponding F
distribution has degrees of freedom,
ν
N
= n
N
-1, and ν
D
= n
D
-1, where n
N
and
n
D
, are the sample sizes corresponding to the variances s
N
2 and s
D
2 ,
respectively.
The following table shows how to select the numerator and denominator for F
o
depending on the alternative hypothesis chosen:
____________________________________________________________________
Alternative
Test Degrees
hypothesis statistic of freedom
____________________________________________________________________
H
1
: σ
1
2 < σ
2
2 (one-sided) F
o
= s
2
2 /s
1
2 ν
N
= n
2
-1, ν
D
= n
1
-1
H
1
: σ
1
2 > σ
2
2 (one-sided) F
o
= s
1
2 /s
2
2 ν
N
= n
1
-1, ν
D
= n
2
-1
H
1
: σ
1
2 ≠σ
2
2 (two-sided) F
o
= s
M
2 /s
m
2 ν
N
= n
M
-1, ν
D
= n
m
-1
s
M
2 =max(s
1
2 ,s
2
2 ), s
m
2 =min(s
1
2 ,s
2
2 )
___________________________________________________________________
(*) n
M
is the value of n corresponding to the s
M
, and n
m
is the value of n
corresponding to s
m
.
____________________________________________________________________
The P-value is calculated, in all cases, as: P-value = P(F>F
o
) = UTPF( ν
N
, ν
D
,F
o
)
The test criteria are:
•
Reject H
o
if P-value < α
• Do not reject H
o
if P-value > α.